Kinetic Energy from a Simple Harmonic motion and spring

[Brittany King]

Homework Statement

A 0.26-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 190 N/m. The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the displacement is x = 1.4×10−2 m, what is the kinetic energy of the block?

Homework Equations

KE=1/2mw^2A^2sin^2(wt+phi)
a=(k/m)x
w=(k/m)^1/2

The Attempt at a Solution

I have everything for the equation except for phi and and the amplitude A. I have found a=10.23 m/s2 and w=27.0327rad/s but I am stuck on how to find phi and A. Is there a relationship between the initial equilibrium position for finding A or phi?

Thanks for the help!

 

[BiGyElLoWhAt]

What's wrong with $PE = 1/2 k x^2$?
You have the amplitude, so you know the total energy. (Yes, you do have the amplitude)

 

[cnh1995]

Is there a relationship between the initial equilibrium position for finding A or phi?

You do have A.

The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest

KE=1/2mw^2A^2sin^2(wt+phi

What will be the KE of the block at t=0? Put it in this equation to get phi.

 

[Brittany King]

What's wrong with $PE = 1/2 k x^2$?
You have the amplitude, so you know the total energy. (Yes, you do have the amplitude)

To use PE=1/2kx^2 wouldn't I need the x at

You do have A.What will be the KE of the block at t=0? Put it in this equation to get phi.

Is A= 0.014m?

 

[Brittany King]

To use PE=1/2kx^2 wouldn't I need the x at 0.014m? If that is my A?Is A= 0.014m?

 

[BiGyElLoWhAt]

No. When it's stretched initially, prior to letting go, what is the KE? At which point in the cycle of a general harmonic oscillator is the KE equal to this value?

Then you're looking for the KE at the point x = .014m. So you know x for the PE, as you know at which point you want to look at.

 

[Brittany King]

No. When it's stretched initially, prior to letting go, what is the KE? At which point in the cycle of a general harmonic oscillator is the KE equal to this value?

Then you're looking for the KE at the point x = .014m. So you know x for the PE, as you know at which point you want to look at.

Oh I got it now! Thanks so much ! :)

 

[BiGyElLoWhAt]

No problem.