Simple Harmonic Motion - basic question

[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?

 

[Doc Al]

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?

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.

 

[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!