Question: Use Mathematica to obtain a numerical solution to the pendulum equation in the previous problem without approximation for the case that L = 1.000 m

Use Mathematica to obtain a numerical solution to the pendulum equation in the previous problem without approximation for the case that L = 1.000 m with the initial conditions ϕ(0) = 0.350 rad (about 20◦) and dϕ/dt = 0. Evaluate the solution for t = 0.500 s, 1.000 s, and 1.500 s. Make a graph of your solution for 0 < t < 4.00 s. Repeat your solution for ϕ(0) = 0.050 rad (about 2.9^◦) and dϕ/dt = 0. Determine the period and the frequency from your graphs. How do they compare with the solution from the previous problem?

Step by Step Solution

★★★★★

3.31 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

From the graph the period appears to be about 21 s From t... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Physical Chemistry Questions!

Use Mathematica to obtain a numerical solution to the differential equation in the previous problem for the range 0

Use a numerical solver to obtain a numerical solution curve for the given initial-value problem. First use Eulers method and then the RK4 method. Use h = 0.25 in each case. Superimpose both solution...

In our example of the free-falling parachutist, we assumed that the acceleration due to gravity was a constant value of 9.8 m/s 2 . Although this is a decent approximation when we are examining...

Can someone help me by answering this exercises of a pendulum for the subject of NUMERICAL METHODS IN ENGINEERING Thanks a lot One of the fundamental systems in physics is the simple pendulum. This...

Can someone please answer the following question using MATLAB language? Can you please comment your code and post a picture of part 1 , that would be very helpful. I apologize for posting such a long...

6. " In this problem, we'll look at the effect of a periodic external force on the pendu- lum, using the model 0" + 0.050' + sin 0 = 0.3 cos wt (D.5) (cf. Problems 3-5). We have chosen a value for...

Construct a computer program that uses both the secant method and the Runge-Kutta method (that you developed in assignment #3) to obtain a numerical solution to the two-point boundary-value problem:...

function LAB04ex1 %NOTE: you CAN run this type of function m file as a script because it requires no inputs. Click the Green arrow above the "Run" tab t0 = 0; tf = 40; %initial and final time y0 =...

MATLAB sessions: Laboratory 4 MAT 275 Laboratory 4 MATLAB solvers for First-Order IVP In this laboratory session we will learn how to 1. Use MATLAB solvers for solving scalar IVP 2. Use MATLAB...

function = explicit(mx) %% Problem Number: 49 L = 45; tmax = 80; U = 0.8; D = 1.2; Xs = 4; Cs = 10; XFlux = 36; % % % % % % % m s m/s m2/s m kg/m m % Calculating dx and dt based of mx input dx =...

You want to evaluate three mutual funds using the information ratio measure for performance evaluation. The average risk-free return during the sample period is 3% p.a., and the average return on the...

Open Outcry Corp. has declared a regular quarterly dividend of $1.35 per share. The current share price is $15.00 per share. Regular dividends are taxed at 15%, which will be withheld on the payment...

Given someone with a gross income of $ 1 2 0 , 0 0 0 and nondiscretionary expenses of $ 3 2 , 0 0 0 , discretionary expenses of $ 1 0 , 0 0 0 and capital expenditures on leisure items of $ 5 , 0 0 0...

. Is there a necessity for manufacturers to partner up with retailers in order to devise an effective CRM strategy?

What parametric test can be used to compare the 16Î±-OHE 1 percentages on a high-fat diet vs. a low-fat diet? Endocrinology A study to assess the effect of a low-fat diet on estrogen...

Perform the test in Problem 9.61, and report a p-value (two-tailed)? Endocrinology A study to assess the effect of a low-fat diet on estrogen metabolism recruited 6 healthy women ages 2132 [5]. The...

What nonparametric test can be used to compare the 16Î±-OHE 1 percentages on a high-fat diet vs. a low-fat diet? Endocrinology A study to assess the effect of a low-fat diet on estrogen...

one or two sentences explaining each line from "previous close" to "1yr target est" 239.989.04(3.63%) As of 1:02PM EDT. Market open. Please explain each line in the data provided for the FedEx...

Use graphical approximation techniques to answer the question When would an ordinary annuity consisting of quarterly payments of $570.40 at 8% compounded quarterly be worth more than a principal of...

A project has 80 activities. At the end of period 11, activity A is 100% completed, activity B is 70% completed, activity C is 60% completed, and activity D is 90% completed. The budgeted costs for...