# Equation of motion, functions

Not what you're looking for?

A simple harmonic oscillator, of mass m and natural frequency w_0, experiences an oscillating driving force f(t)=m a cos(wt). Therefore, its equation of motion is

d^2x/dt^2 + w^2_0x = acos(wt)

where x is the position. Given that at t=0 we have x=dx/dt=0, find the function x(t). Use BOTH with variation of the parameters and guessing methods. Describe the solution if w is approximately, but not exactly, equal to w_0. Give an example of a physical system where this happens.

##### Purchase this Solution

##### Solution Summary

The expert examines equation of motion and functions.

##### Solution Preview

Hello and thank you for posting your question to BrainMass.

The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

Feedback is always appreciated.

The equation is:

(1.1)

The general solution is given by:

(1.2)

Where is the solution of the associated homogenous equation

(1.3)

and is a particular solution to equation (1.1).

This equation is a second order linear equation with constant coefficients.

To solve equation (1.3) we "guess" a solution in the form:

(1.4)

Plugging it in the homogenous solution we get:

(1.5)

Where

Thus the two homogenous solutions are:

(1.6)

Since we are interested in real solutions, and the homogenous solution is a linear combination of these two linearly solutions, we can use Euler's identity

(1.7)

To express the two ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### 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.

##### Intro to the Physics Waves

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

##### 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.

##### Basic Physics

This quiz will test your knowledge about basic Physics.

##### The Moon

Test your knowledge of moon phases and movement.