# Simple harmonic motion and amplitude

1. Jul 22, 2004

### wilmerena

I have a short question:

an object undergoes simple harmonic motion with a period T and amplitude A. How long does it take the object to travel from x = A to x = A/2 ?

the answer is T/6, but im not sure how to get to that,

Do I get it from x = Acos(2pi/T xt)?
help

2. Jul 22, 2004

### jamesrc

You could (but I wouldn't use an x to stand for multiplication especially in an equation that already has an x in it). You could solve for t when x = A and when x = A/2 and find the difference in times.

You know that x = A at t = 0.

for x = A/2:

$$x = \frac A 2 = A\cos \left( \frac{2\pi t}{T} \right )$$

The cosine of 60 degrees is 1/2, so this reduces to:

$$\frac \pi 3 = \frac{2\pi t}{T}$$

Solve for t and you'll find the answer.

3. Jul 22, 2004

### wilmerena

thanks so much