# Amount of time for a half period to occur

## Homework Statement

A mass-spring system has k = 105 N/m and m = 1.75 kg.

If it is undergoing simple harmonic motion, how much time does it take the mass to go from x = A to x = 0?

T=2pi*sqrt(m/k)

## The Attempt at a Solution

Tried plugging in the values for the equation I gave to find T, then cutting it in half to find the amount of time the question asked for, but it's not the correct answer.

vela
Staff Emeritus
Homework Helper
What exactly is one cycle? If you understand that, you'll see why your answer is wrong. It may help to look at a diagram that shows one period in your textbook.

When the mass goes into the spring and back?

ehild
Homework Helper
Sketch the x(t) function for a full period and see.

ehild

vela
Staff Emeritus
Homework Helper
When the mass goes into the spring and back?
Yes. So in one cycle, if it starts at x(0)=A, it ends at x(T)=A, but more important, what does x(t) do in between? As ehild suggested, plot x(t) for one cycle.

dextercioby
Homework Helper
Who's A and can you link it to T ? EDIT: So A's the amplitude...

Last edited:
Uhh x goes to A? Which equation can I use to solve for that? x=Acos(ωt)?

Sorry I'm braindead been studying all morning I just want this homework done.

ehild
Homework Helper
Which equation can I use to solve for that? x=Acos(ωt)?

Yes. x = A cos (2pi* t/T). How does it look like? What is x at t=0, t=T/8, T/4, ...

ehild

So I can plug in x as A so that A cancels out here and then solve for t where T = 1/2?

ehild
Homework Helper
So I can plug in x as A so that A cancels out here and then solve for t where T = 1/2?

Is T=1/2???????