The motion equation of damped mass-spring system as shown in Fig. 1 below is given as...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The motion equation of damped mass-spring system as shown in Fig. 1 below is given as follows: d²x dx +c dt² dt m- + kx = f(t),t> 0 where: x(t): displacement in meters. m: mass in kg. c: damping coefficient in kg/s. k: spring stiffness constant in N/m. t: time in seconds. f(t): external force applied on system in N. k f(t) m C Assume that: m = 2 kg, c = 3 kg/s, k = 20 N/m. Initially, assume f(t) = 0. X(t) Fig. 1: Damped mass-spring system. (1-a) Determine the general solution of x(t). (1-b) Given the initial conditions x (0) = 4, and x'(0) = 1, determine the particular solution of x(t). (1-c) Use Laplace transform to solve the given differential equation with the same initial conditions given in (1-b). (1-d) Critically evaluate how your mathematical solution behaves in transient and steady state regions. (1-e) Build a Simulink block model of the system, and generate the results of the differential equation. Show the model and the results in your report and specify the transient and steady state regions. Make sure you submit the simulation file (properly named). (1-f) Assume now that the external force f(t) equals 10 N, repeat all parts (1-a,b,c,d,e). The motion equation of damped mass-spring system as shown in Fig. 1 below is given as follows: d²x dx +c dt² dt m- + kx = f(t),t> 0 where: x(t): displacement in meters. m: mass in kg. c: damping coefficient in kg/s. k: spring stiffness constant in N/m. t: time in seconds. f(t): external force applied on system in N. k f(t) m C Assume that: m = 2 kg, c = 3 kg/s, k = 20 N/m. Initially, assume f(t) = 0. X(t) Fig. 1: Damped mass-spring system. (1-a) Determine the general solution of x(t). (1-b) Given the initial conditions x (0) = 4, and x'(0) = 1, determine the particular solution of x(t). (1-c) Use Laplace transform to solve the given differential equation with the same initial conditions given in (1-b). (1-d) Critically evaluate how your mathematical solution behaves in transient and steady state regions. (1-e) Build a Simulink block model of the system, and generate the results of the differential equation. Show the model and the results in your report and specify the transient and steady state regions. Make sure you submit the simulation file (properly named). (1-f) Assume now that the external force f(t) equals 10 N, repeat all parts (1-a,b,c,d,e).
Expert Answer:
Posted Date:
Students also viewed these mathematics questions
-
x1 - 3x2 + x3 = 4 2x1 - x2 = - 2 4x1 - 3x3 = 0 Solve by Cramer's rule, where it applies.
-
X1 and X2 are independent n(0, Ï2) random variables. (a) Find the joint distribution of Y1 and Y2, where (b) Show that Yi and Y2 are independent, and interpret this result geometrically. - 3 +...
-
x1 + 3x2 + x3 = 4 2x1 + 2x Solve the system by inverting the coefficient matrix and using Theorem 1.6.2.
-
An analog filter is defined by its transfer function: 100n H(s) = %3D s+ 100n What type of filter H(s) is? A. Low-pass B. High-pass C. Band-pass D. Band-stop
-
Imagine a study being conducted by a senior manager at Apple who is interested in driving more business through iTunes. The managers ideas require a huge capital investment and are predicated on...
-
Use the data in HPRICE1.RAW for this exercise. (i) Estimate the model price = (0 + (1 lotsize + (2 sqrft + (3 bdrms + u and report the results in the usual form, including the standard error of the...
-
Using the information in the Application "Botox and Price Discrimination," determine how much Allergan loses by being a single-price monopoly rather than a perfectly price-discriminating monopoly....
-
Compound A (C10H15N) is soluble in dilute HCl. The IR absorption spectrum shows two bands in the 3300-3500-cm-1 region. The broadband proton-decoupled 13C spectrum of A is given in Fig. 20.8. Propose...
-
Superior Company provided the following data for the year ended December 3 1 ( all raw materials are used in production as direct materials ) : Selling expenses $ 2 1 7 , 0 0 0 Purchases of raw...
-
A propped cantilever beam of length 2L is loaded by a uniformly distributed load with intensity q. The beam is supported at B by a linearly elastic spring with stiffness k. Use the method of...
-
Tricia and Janine are roommates and leave Houston on Interstate 10 at the same time to visit their families for a long weekend. Tricia travels west and Janine travels east. If Tricias average speed...
-
Question: ABC Investments, an active investment management firm, is increasing the proportion of their portfolios invested in equities relative to their short and long term bonds. Determine the...
-
Financial indicators are impacted by the indicators of capacity, , and performance. The costs of resources used in providing nursing care the supplies required are known as what?
-
What is the liquidity position of the company you are analyzing? 2) What is the liquidity trend of the company you are analyzing? 3) Based on your analysis, what is your recommendation to investors:...
-
Barry is currently registered as a Maryland tax preparer. A longtime client has written him requesting a copy of their 2020 and 2021 returns because their copies were lost in a fire. What...
-
What is a possible outcome of the Release activity? Explain briefly
-
What is the primary strength of standardized questionnaires in terms of measurement? Flexibility Reliability Validity Ability to customize questions for each respondent
-
TRUE-FALSE QUESTIONS 1. In terms of preliminary analytical procedures, assume that the company has introduced a new product with a low price point and significant customer demand. The auditor would...
-
Apple stock is selling for \($120\) per share. Call options with a \($117\) exercise price are priced at \($12.\) What is the intrinsic value of the option, and what is the time value?
-
Refer to Problem 14.9. What would the loss of the seller of the put option be if, at expiration, XLB is trading at \($20?\) What would the profit of the seller be if, at expiration, XLB is trading at...
-
Ibrahim bought 200 shares of a stock trading in the Abu Dhabi Securities Exchange at AED 12 (United Arab Emirates dirham) per share. Over time, the price of the stock increased to AED 18 per share....
Study smarter with the SolutionInn App