# SHO: Find amplitude given k, and x,v,a at unknown time

1. Oct 11, 2011

### jdp1991

1. The problem statement, all variables and given/known data

A block attached to a spring is experiencing simple harmonic motion. You know the value of postion, velocity, and acceleration at an unknown time. Find the period of oscillation, the mass of the block, and the amplitude of oscillation.

We were given values for k, x, v, a

2. Relevant equations
F=ma=kx
Tspring=2∏√(m/k)
x=Acos(ωt+phi)

3. The attempt at a solution
This was the final question on an exam I just took and I was baffled about how to find Amplitude. We were given values for position, velocity, and acceleration, but I cannot remember what they were off the top of my head, so an algebraic solution is fine.

I started my finding the mass of the block by setting kx=ma: m=kx/a

I then plugged that value for m into the spring period equation: T=2∏√((kx/a)/k)=2∏√(x/a)

The previous two I'm not confident about, but I was completely lost when asked to find the amplitude.

Thanks

EDIT: The problem takes place on a horizontal plane (a flat frictionless surface)

Last edited: Oct 11, 2011
2. Oct 11, 2011

### SammyS

Staff Emeritus
How are velocity and acceleration related to the position?

3. Oct 11, 2011

### Villyer

Is this on a horizontal or vertical plane?

4. Oct 11, 2011

### jdp1991

velocity = dx/dt and acceleration = d2x/dt2?
So v = -ωAsin(ωt+phi)
and a = -ω2Acos(ωt+phi)

Sorry horizontal

5. Oct 11, 2011

### SammyS

Staff Emeritus
So, a/x = -ω2 . Gives you ω.

Then x2 + (v/ω)2 = A2

6. Oct 11, 2011

### jdp1991

ok that makes sense

maybe i'm missing something obvious, but how did you get this?

7. Oct 11, 2011

### Villyer

Still a little lost :3

8. Oct 11, 2011

### jdp1991

OOPS! Haha sorry it should be horizontal.

9. Oct 11, 2011

### SammyS

Staff Emeritus
Did you try it.

sin2(θ) + cos2(θ) = 1