Simple harmonic motion: find amplitude given k, x, v, and a

[jdp1991]

Homework Statement

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

Homework Equations

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

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)

 

[SammyS]

How are velocity and acceleration related to the position?

 

[Villyer]

Is this on a horizontal or vertical plane?

 

[jdp1991]

How are velocity and acceleration related to the position?

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

Is this on a horizontal or vertical plane?

Sorry horizontal

 

[SammyS]

So, a/x = -ω² . Gives you ω.

Then x² + (v/ω)² = A²

 

[jdp1991]

So, a/x = -ω² . Gives you ω.

ok that makes sense

Then x² + (v/ω)² = A²

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

 

[Villyer]

EDIT: The problem takes place on a vertical plane

Sorry horizontal

Still a little lost :3

 

[jdp1991]

Still a little lost :3

OOPS! Haha sorry it should be horizontal.

 

[SammyS]

So, a/x = -ω² . Gives you ω.

Then x² + (v/ω)² = A²

ok that makes sense

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

Did you try it.

sin²(θ) + cos²(θ) = 1