# Homework Help: Simple Harmonic Motion - basic question

1. Apr 5, 2012

### oakk

A mass on a spring undergoes simple harmonic motion with amplitude A.
a) In a time equal to three periods, what is the magnitude of the displacement of the mass?
b) In a time equal to three periods, what actual distance did it travel?

In the first part, I was at first trying to use an equation but realized that wasn't necessary. If it completes three full periods, it ends up at the same position it started at.

But I don't understand how to calculate the second part. I was trying to use the equation x(t)=Acos(wt) to find the distance traveled, but I don't know t, nor do I know if this is even the right method for solving this. How am I supposed to know the actual distance traveled?

2. Apr 5, 2012

### Staff: Mentor

It's simpler than all that. Just imagine the mass bouncing up and down. Start at the top. Where is it? (With respect to the equilibrium position.) After half a period, where is it? How far has it traveled? After 1 period, where is it? And so on.

3. Apr 5, 2012

### oakk

Ah, ok. That makes much more sense. I think my problem is that I wasn't actually envisioning the mass with its simple up/down motion, but rather focusing too much on the sine waves. Thanks!