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bpw91284 · 2008-03-25 04:55:49

1. The problem statement, all variables and given/known data
A ball bounces up and down off the ground and each bounce it returns to the same height. Is this simple harmonic motion?

2. Relevant equations
None

3. The attempt at a solution
I don't think it is because in simple harmonic motion the maximun velocity occurs in the middle of the amplitudes but for the bouncing ball it occurs right before and right after it hits the ground. If that is correct, can someone explain it better?

Chris · 2008-03-25 16:22:06

Simple harmonic motion is defined by a very specific differential equation:

$m\frac{d^2x}{dt^2} = -kx$

or,

$ma = -kx$

The solution to this differential equation is sinusoidal. The equation above basically states that for simple harmonic motion, the force is proportional to and opposite in direction to the displacement from equillibrium.

You are right that a bouncing ball is not simple harmonic; however, I'm not sure if your reasoning is correct. If the floor is your equilibrium point, then you would have maximum velocity right before and right after the equillibrium position.

The bouncing ball is not simple harmonics because the force (gravity) is not always opposite in direction to the displacement from equillibrium.

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#1 2008-03-25 04:55:49

Simple Harmonic Motion

#2 2008-03-25 16:22:06

Re: Simple Harmonic Motion

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