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engineering
introduction mechanical engineering

Introduction To MATLAB For Engineers 3rd Edition William Palm III - Solutions

A robot rotates about its base at 2 rpm while lowering its arm and extending its hand. It lowers its arm at the rate of 120° per minute and extends its hand at the rate of 5 m/min. The arm is 0.5 m long. The xyz coordinates of the hand are given by where t is time in minutes.Obtain the
The popular amusement ride known as the corkscrew has a helical shape. The parametric equations for a circular helix arex = a cos ty = a sin tz = btwhere a is the radius of the helical path and b is a constant that determines the “tightness” of the path. In addition, if b > 0, the helix has
An approximation to the function sin x is sin x ≈ x - x3/6. Plot the sin x function and 20 evenly spaced error bars representing the error in the approximation.
The circuit shown in Figure P26 consists of a resistor and a capacitor and is thus called an RC circuit. If we apply a sinusoidal voltage υi, called the input voltage, to the circuit as shown, then eventually the output voltage !o will be sinusoidal also, with the same frequency but with a
Figure P25 is a representation of an electrical system with a power supply and a load. The power supply produces the fixed voltage υ1 and supplies the current i1 required by the load, whose voltage drop is υ2. The current voltage relationship for a specific load is found from experiments to
The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by where n is the number of times per year the interest is compounded. For continuous compounding, A = Pert. Suppose $10 000 is initially invested at 3.5 percent (r = 0.035).a. Plot A
The volume V and surface area A of a sphere of radius r are given by a. Plot V and A versus r in two subplots, for 0.1 ≤ r ≤ 100 m. Choose axes that will result in straight-line graphs for both V and A.b. Plot V and r versus A in two subplots, for 1 ≤ A ≤ 104 m2. Choose axes that will
A sum of $10 000 invested at 4 percent interest compounded annually will grow according to the formulay(k) = 104(1.04)kwhere k is the number of years (k = 0, 1, 2, . . .). Plot the amount of money in the account for a 10-year period. Do this problem with four types of plots: the xy plot, the stem
The following table shows the average temperature for each year in a certain city. Plot the data as a stem plot, a bar plot, and a stairs plot. Year 2000 2001 2002 2003 2004 Temperature (°C) 21 18 19 20 17
When a constant voltage was applied to a certain motor initially at rest, its rotational speed s(t) versus time was measured. The data appear in the following table:Determine whether the following function can describe the data. If so, find the values of the constants b and c.s(t) = b(1 - ect) Time
Oscillations in mechanical structures and electric circuits can often be described by the functionwhere t is time and ( is the oscillation frequency in radians per unit time. The oscillations have a period of 2π/ω, and their amplitudes decay in time at a rate determined by τ, which is called the
The perfect gas law relates the pressure p, absolute temperature T, mass m, and volume V of a gas. It states thatPV = mRTThe constant R is the gas constant. The value of R for air is 286.7 (N · m)/(kg · K). Suppose air is contained in a chamber at room temperature (20°C = 293 K). Create a plot
The height h(t) and horizontal distance x(t) traveled by a ball thrown at an angle A with a speed ! are given byAt Earth’s surface the acceleration due to gravity is g % 9.81 m/s2.a. Suppose the ball is thrown with a velocity υ = 10 m/s at an angle of 35+. Use MATLAB to compute how high the ball
In certain kinds of structural vibrations, a periodic force acting on the structure will cause the vibration amplitude to repeatedly increase and decrease with time. This phenomenon, called beating, also occurs in musical sounds. A particular structure’s displacement is described bywhere y is the
The following functions describe the oscillations in electric circuits and the vibrations of machines and structures. Plot these functions on the same plot. Because they are similar, decide how best to plot and label them to avoid confusion. x(t) 10e 0.5t -0.51 sin(3t + 2) y(t) = Te 04 cos(5t - 3)
The function y(t) = 1 -! e-bt, where t is time and b > 0, describes many processes, such as the height of liquid in a tank as it is being filled and the temperature of an object being heated. Investigate the effect of the parameter b on y(t). To do this, plot y versus t for several values of b
Use a plot over the range 0 ≤ x ≤ 5 to con rm that sin( ix) = i sinh x.
The complex number identity eix = cos x + i sin x is often used to convert the solutions of equations into a form that is relatively easy to visualize. Con rm this identity by plotting the imaginary part versus the real part for both the left and right sides over the range 0 ≤ x ≤ 2π.
You can use trigonometric identities to simplify the equations that appear in many applications. Con rm the identity tan(2 x) = 2 tan x/(1 - tan2 x) by plotting both the left and the right sides versus x over the range 0 ≤ x ≤ 2$.
Many applications use the following “small angle” approximation for the sine to obtain a simpler model that is easy to understand and analyze. This approximation states that sin x ≈ x, where x must be in radians. Investigate the accuracy of this approximation by creating three plots. For the
Plot columns 2 and 3 of the following matrix A versus column 1. The data in column 1 are time (seconds). The data in columns 2 and 3 are force (newtons). 0 -7 6. 5 -4 3 A A =| 10 -1 9. 15 1 20 -1 2.
A certain shing vessel is initially located in a horizontal plane at x = 0 and y = 10 mi. It moves on a path for 10 hr such that x = t and y = 0.5t2 + 10, where t is in hours. An international shing boundary is described by the line y = 2x + 6.a. Plot and label the path of the vessel and the
It is known that the following Leibniz series converges to the value π/4 as n → ). Plot the difference between π/4 and the sum S(n) versus n for 0 ≤ n ≤ 200. 1 S(n) = E(-1)*- k=0 2k + 1
Using estimates of rainfall, evaporation, and water consumption, the town engineer developed the following model of the water volume in the reservoir as a function of time where V is the water volume in liters and t is time in days. Plot V(t) versus t. Use the plot to estimate how many days it
Cables are used to suspend bridge decks and other structures. If a heavy uniform cable hangs suspended from its two endpoints, it takes the shape of a catenary curve whose equation iswhere a is the height of the lowest point on the chain above some horizontal reference line, x is the horizontal
To compute the forces in structures, sometimes we must solve equations similar to the following. Use the fplot function to find all the positive roots of this equation:x tan x = 9
a. Estimate the roots of the equationby plotting the equation.b. Use the estimates found in part a to nd the roots more accurately with the fzero function. TTX 2 - 3x + 5x sin 4 + 3 = 0 4
Consider the following costs for a certain chemical product:Fixed cost: $2.045 million/year.Variable costs:Material cost: 62 cents per gallon of product.Energy cost: 24 cents per gallon of product.Labor cost: 16 cents per gallon of product.Assume that we produce only what we sell. Let P be the
Breakeven analysis determines the production volume at which the total production cost is equal to the total revenue. At the breakeven point, there is neither pro t nor loss. In general, production costs consist of fixed costs and variable costs. Fixed costs include salaries of those not directly
Redo Problem 48 with the restriction that the next week’s production is set to zero if the inventory exceeds 40 carts.Problem 48A certain company manufactures and sells golf carts. At the end of each week, the company transfers the carts produced that week into storage (inventory). All carts that
A certain company manufactures and sells golf carts. At the end of each week, the company transfers the carts produced that week into storage (inventory). All carts that are sold are taken from the inventory. A simple model of this process isI(k + 1) = P(k) + I(k) - S(k)WhereP(k) = number of carts
Suppose you project that you will be able to deposit the following monthly amounts into a savings account for a period of 5 years. The account initially has no money in it.At the end of each year in which the account balance is at least $3000, you withdraw $2000 to buy a certificate of deposit
Using the program developed in Problem 19, write a program that uses the switch structure to compute the number of days in a year up to a given date, given the year, the month, and the day of the month.Write a program that accepts a year and determines whether the year is a leap year. Use the mod
Consider the college enrollment model discussed in Example 4.9–2. Suppose the college wants to limit freshman admissions to 120 percent of the current sophomore class and limit sophomore transfers to 10 percent of the current freshman class. Rewrite and run the program given in the example to
Engineers often need to estimate the pressures and volumes of a gas in a container. The van der Waals equation is often used for this purpose. It is where the term b is a correction for the volume of the molecules and the term a/V̂2 is a correction for molecular attractions. The gas constant
The height and speed of a projectile (such as a thrown ball) launched with a speed of υ0 at an angle A to the horizontal are given by where g is the acceleration due to gravity. The projectile will strike the ground when h(t) = 0, which gives the time to hit thit = 2(υ0/g)sinA.Use the switch
Use the switch structure to write a MATLAB program to compute the amount of money that accumulates in a savings account in one year. The program should accept the following input: the initial amount of money deposited in the account; the frequency of interest compounding (monthly, quarterly,
The following table gives the approximate values of the static coefficient of friction 1 for various materials.Materials ................................ µMetal on metal .................... 0.20Wood on wood .................... 0.35Metal on wood ..................... 0.40Rubber on concrete
Assume that the human player makes the first move against the computer in a game of Tic-Tac-Toe, which has a 3 x 3 grid. Write a MATLAB function that lets the computer respond to that move. The function’s input argument should be the cell location of the human player’s move. The function’s
Consider the following script file. Fill in the lines of the following table with the values that would be displayed immediately after the while statement if you ran the script file. Write in the values the variables have each time the while statement is executed. You might need more or fewer lines
Many applications require us to know the temperature distribution in an object. For example, this information is important for controlling the material properties, such as hardness, when cooling an object formed from molten metal. In a heat-transfer course, the following description of the
The equations describing the circuit shown in Figure P37 area. The given values of the resistances and the voltage υ1 are R1 = 5. R2 = 100, R3 = 200, R4 = 150, R5 = 250 kΩ, and υ1 = 100V.(Note that 1 kΩ = 1000 0.) Suppose that each resistance is rated to carry a current of no more than 1 mA (=
In the structure in Figure P36a, six wires support three beams. Wires 1 and 2 can support no more than 1200 N each, wires 3 and 4 can support no more than 400 N each, and wires 5 and 6 can support no more than 200 N each. Three equal weights W are attached at the points shown. Assuming that the
A weight W is supported by two cables anchored a distance D apart (see Figure P35). The cable length LAB is given, but the length LAC is to be selected. Each cable can support a maximum tension force equal to W.Figure P35. For the weight to remain stationary, the total horizontal force and
Use a loop in MATLAB to determine how long it will take to accumulate $1 000 000 in a bank account if you deposit $10 000 initially and $10 000 at the end of each year; the account pays 6 percent annual interest.
One bank pays 5.5 percent annual interest, while a second bank pays 4.5 percent annual interest. Determine how much longer it will take to accumulate at least $50 000 in the second bank account if you deposit $1000 initially and $1000 at the end of each year.
Use a while loop to determine how many terms in the series 2k, k = 1, 2, 3, . . . , are required for the sum of the terms to exceed 2000. What is the sum for this number of terms?
Plot the function y = 10(1 = e-x/4) over the interval 0 ≤ x ≤ xmax, using a while loop to determine the value of xmax such that y(xmax) = 9.8.Properly label the plot. The variable y represents force in newtons, and the variable x represents time in seconds.
A certain company makes televisions, stereo units, and speakers. Its parts inventory includes chassis, picture tubes, speaker cones, power supplies, and electronics. The inventory, required components, and profit for each product appear in the following table. Determine how many of each product to
A company has the choice of producing up to four different products with its machinery, which consists of lathes, grinders, and milling machines. The number of hours on each machine required to produce a product is given in the following table, along with the number of hours available per week on
A company wants to locate a distribution center that will serve six of its major customers in a 30 × 30 mi area. The locations of the customers relative to the southwest corner of the area are given in the following table in terms of (x, y) coordinates (the x direction is east; the y direction is
a. An ideal diode blocks the flow of current in the direction opposite that of the diode’s arrow symbol. It can be used to make a half-wave rectifier as shown in Figure P27a. For the ideal diode, the voltage υL across the load RL is given by Suppose the supply voltage isυs(t) = 3e-t/3
The price, in dollars, of a certain stock over a 10-day period is given in the following array.price = [19, 18, 22, 21, 25, 19, 17, 21, 27, 29]Suppose you owned 1000 shares at the start of the 10-day period, and you bought 100 shares every day the price was below $20 and sold 100 shares every day
Electrical resistors are said to be connected “in series” if the same current passes through each and “in parallel” if the same voltage is applied across each. If in series, they are equivalent to a single resistor whose resistance is given byR = R1 + R2 + R3 + … + RnIf in parallel, their
We want to analyze the mass-spring system discussed in Problem 20 for the case in which the weight W is dropped onto the platform attached to the center spring. If the weight is dropped from a height h above the platform, we can find the maximum spring compression x by equating the weight’s
Consider the array A.Write a program that computes the array B by computing the natural logarithm of all the elements of A whose value is no less than 1, and adding 20 to each element that is equal to or greater than 1. Do this in two ways:a. By using a for loop with conditional statements.b. By
The (x, y) coordinates of a certain object as a function of time t are given byx(t) = 5t – 10 y(t) = 25t2 = 120t + 144for 0 ≤ t ≤ 4. Write a program to determine the time at which the object is the closest to the origin at (0, 0). Determine also the minimum distance.Do this in two
Use a for loop to determine the sum of the rst 10 terms in the series 5k3, k % 1, 2, 3, . . . , 10.
Use a for loop to plot the function given in Problem 16 over the interval -2 ≤ x ≤ 6. Properly label the plot. The variable y represents height in kilometers, and the variable x represents time in seconds.
Figure P20 shows a mass-spring model of the type used to design packaging systems and vehicle suspensions, for example. The springs exert a force that is proportional to their compression, and the proportionality constant is the spring constant k. The two side springs provide additional resistance
Write a program that accepts a year and determines whether the year is a leap year. Use the mod function. The output should be the variable extra_day, which should be 1 if the year is a leap year and 0 otherwise. The rules for determining leap years in the Gregorian calendar are as follows:1. All
Write a program that accepts a numerical value x from 0 to 100 as input and computes and displays the corresponding letter grade given by the following table.A. x ≥ 90B. 80 ≤ x ≤ 89C. 70 ≤ x ≤ 79D. 60 ≤ x ≤ 69F. x < 60a. Use nested if statements in your program (do not use
Rewrite the following statements to use only one if statement.if x < yif z < 10w = x*y*zendend
Write a script le using conditional statements to evaluate the following function, assuming that the scalar variable x has a value. The function isY = ex+1 for x < -1, y = 2 + cos(πx) for -1 ≤ x ≤ 5, and y = 10(x - 5) + 1 for x ≥ 5. Use your le to evaluate y for x = -5, x = 3, and x = 15,
Are these following expressions equivalent? Use MATLAB to check your answer for specific values of a, b, c, and d.a. 1. (a == b) & ((b == c)|(a == c))2. (a == b)|((b == c)&(a == c))b. 1. (a < b)&((a > c)|(a > d))2. (a < b)&(a > c)|((a < b)&(a > d))
Let e1 and e2 be logical expressions. DeMorgan’s laws for logical expressions state thatNOT(e1 AND e2) implies that (NOT e1) OR (NOT e2)andNOT(e1 OR e2) implies that (NOT e1) AND (NOT e2)Use these laws to nd an equivalent expression for each of the following expressions and use MATLAB to verify
Suppose that x = [-3, 0, 0, 2, 5, 8] and y = [-5, -2, 0, 3, 4, 10]. Find the results of the following operations by hand and use MATLAB to check your results.a. z = y < ~ xb. z = x & yc. z = x|yd. z = xor(x,y)
The arrays price_A, price_B, and price_C given below contain the price in dollars of three stocks over 10 days.a. Use MATLAB to determine how many days the price of stock A was above both the price of stock B and the price of stock C.b. Use MATLAB to determine how many days the price of stock A was
The arrays price_A and price_B given below contain the price in dollars of two stocks over 10 days. Use MATLAB to determine how many days the price of stock A was above the price of stock B.price_A = [19, 18, 22, 21, 25, 19, 17, 21, 27, 29]price_B = [22, 17, 20, 19, 24, 18, 16, 25, 28, 27]
The array price given below contains the price in dollars of a certain stock over 10 days. Use MATLAB to determine how many days the price was above $20.price = [19, 18, 22, 21, 25, 19, 17, 21, 27, 29]
For the arrays x and y given below, use MATLAB to find all the elements in x that are greater than the corresponding elements in y.x = [-3, 0, 0, 2, 6, 8] y = [-5, -2, 0, 3, 4, 10]
Suppose that x = [10, -2, 6, 5, -3] and y = [9, -3, 2, 5, -1]. Find the results of the following operations by hand and use MATLAB to check your results.a. z = (x < 6)b. z = (x <= y)c. z = (x == y)d. z = (x ~= y)
Find the results of the following operations by hand and use MATLAB to check your results.a. z = 6 > 3 + 8b. z = 6 + 3 > 8c. z = 4 > (2 + 9)d. z = (4 < 7) + 3e. z = 4 < 7 + 3f. z = (4<7)*5g. z = 4<(7*5)h. z = 2/5>=5
Suppose that x = 6. Find the results of the following operations by hand and use MATLAB to check your results.a. z = (x < 10)b. z = (x == 10)c. z = (x >= 4)d. z = (x ~= 7)
It is desired to compute the sum of the first 10 terms of the series14k3 = 20k2 + 5k, k = 1, 2, 3, …a. Develop a pseudocode description of the required program.b. Write and run the program described in part a.
The roots of the quadratic equation ax2 + bx + c = 0 are given by a. Develop a pseudocode description of a program to compute both roots given the values of a, b, and c. Be sure to identify the real and imaginary parts.b. Write the program described in part a and test it for the following
Use a text editor to create a le from the data given in Problem 23, but separate each number with a semicolon. Then use the Import Wizard to load and save the data in the MATLAB variable A.Problem 23.Use a text editor to create a le containing the following data. Then use the load function to load
The volume V and surface area A of a sphere of radius r are given by a. Develop a pseudocode description of a program to compute V and A for 0 ≤ r ≤ 3 m and to plot V versus A.b. Write and run the program described in part a. 4 V 3 2 A = 4Tr?
Enter and save the data given in Problem 23 in a spreadsheet. Then import the spreadsheet le into the MA TLAB variable A. Use MATLAB to compute the sum of each column.Problem 23Use a text editor to create a le containing the following data. Then use the load function to load the le into MATLAB, and
Use a text editor to create a le containing the following data. Then use the load function to load the le into MATLAB, and use the mean function to compute the mean value of each column. 55 42 98 49 39 95 63 51 92 58 45 90
Create a primary function that uses a function handle with a nested function to compute the minimum of the function 20x2 - 200x + 12 over the range 0 ≤ x ≤ 10.
Use a primary function with a subfunction to compute the zeros of the function 3x3 - 12x2 - 33x + 80 over the range $10 ≤ x ≤ 10.
Create four anonymous functions to represent the function 6e3cosx2, which is composed of the functions h(z) = 6ez, g(y) = 3 cos y, and f(x) = x2. Use the anonymous functions to plot 6e3cosx2 over the range 0 ≤ x ≤ 4.
Create an anonymous function for 20x2 - 200x + 3 and use ita. To plot the function to determine the approximate location of its minimumb. With the fminbnd function to precisely determine the location of the minimum
Create an anonymous function for 10e-2x and use it to plot the function over the range 0 ≤ x ≤ 2.
Suppose it is known that the graph of the function y = ax3 + bx2 + cx + d passes through four given points (xi, yi ), i = 1, 2, 3, 4. Write a userdefined function that accepts these four points as input and computes the coefficients a, b, c, and d. The function should solve four linear equations in
A torus is shaped like a doughnut. If its inner radius is a and its outer radius is b, its volume and surface area are given by a. Create a user-defined function that computes V and A from the arguments a and b.b. Suppose that the outer radius is constrained to be 2 in. greater than the inner
The volume V and paper surface area A of a conical paper cup are given bywhere r is the radius of the base of the cone and h is the height of the cone.a. By eliminating h, obtain the expression for A as a function of r and V.b. Create a user-defined function that accepts R as the only argument and
Using estimates of rainfall, evaporation, and water consumption, the town engineer developed the following model of the water volume in the reservoir as a function of time where V is the water volume in liters, t is time in days, and r is the town’s consumption rate in liters per day. Write
A fenced enclosure consists of a rectangle of length L and width 2R and a semicircle of radius R, as shown in Figure P13. The enclosure is to be built to have an area A of 2000 ft2. The cost of the fence is $50 per foot for the curved portion and $40 per foot for the straight sides. Use the fminbnd
A fence around a field is shaped as shown in Figure P12. It consists of a rectangle of length L and width W, and a right triangle that is symmetrical about the central horizontal axis of the rectangle. Suppose the width W is known (in meters) and the enclosed area A is known (in square meters).
A water tank consists of a cylindrical part of radius r and height h and a hemispherical top. The tank is to be constructed to hold 600 m3 when filled. The surface area of the cylindrical part is 2πrh, and its volume is πr2h. The surface area of the hemispherical top is given by 2πr2, and its
An object thrown vertically with a speed υ0 reaches a height h at time t, where Write and test a function that computes the time t required to reach a specified height h, for a given value of υ0. The function’s inputs should be h, υ0, and g. Test your function for the case where h = 100
Write a function that accepts temperature in degrees Fahrenheit (°F) and computes the corresponding value in degrees Celsius (°C). The relation between the two isBe sure to test your function. 5 등 (T°F-32) T°C %3D
The output of the MATLAB atan2 function is in radians. Write a function called atan2d that produces an output in degrees.
When a belt is wrapped around a cylinder, the relation between the belt forces on each side of the cylinder isF1 = F2eµβwhere β is the angle of wrap of the belt and & is the friction coefficient. Write a script le that first prompts a user to specify β, µ, and F2 and then computes the
The capacitance of two parallel conductors of length L and radius r, separated by a distance d in air, is given by where ∈ is the permittivity of air (∈ = 8.854 × 10-12 F/m).Write a script le that accepts user input for d, L, and r and computes and displays C. Test the le
For several values of x, use MATLAB to con rm that cosh-1 x = ln(x + √x2 - 1), x ≤ 1
For several values of x, use MATLAB to con rm that sinh x = (ex – e-x)/2.
Use MATLAB to find the angles corresponding to the following coordinates. Hand-check the answers.a. (x, y) = (5, 8)b. (x, y) = (-5, 8)c. (x, y) = (5, -8)d. (x, y) = (-5, -8)

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