Simple harmonic motion and amplitude of an object

[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 I am not sure how to get to that,

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

 

[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.

 

[wilmerena]

thanks so much