Purchase Solution

Simple Harmonic Motion: Write a program to integrate an equation

Not what you're looking for?

Ask Custom Question

See the attached file for the formulas.

Determine an appropriate step size h by assuming that an h that works as expected for simple harmonic motion is good enough for the given initial angle. In particular, if the position at the end of one period is within 0.1% of the original point, we'll be satisfied.

Attachments
Purchase this Solution

Solution Summary

The solution provides good explanations and alternative methods used in solving the problems.

Solution Preview

See attached file.

I chose to solve this using Euler's method. First you have to convert the second-order ODE into two first-order ODEs.

Let v = theta'

Since theta'' = v', v' = -(g/l)*theta.

With me this far? Please try to make the above make sense to you. All we are doing is breaking the problem up into two smaller problems.

Now we have to iterate with the following (where i denotes the discrete time interval):

theta[i+1] = ...

Purchase this Solution


Free BrainMass Quizzes
Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

The Moon

Test your knowledge of moon phases and movement.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.