Calculating Maximum Kinetic Energy of a Vibrating Ball

[rr263]

Homework Statement

A 2.55 kg ball is attached to an unknown spring and allowed to oscillate. The figure shows a graph of the ball’s position x as a function of time . (A)What is the maximum kinetic energy of the vibrating ball? give answer in joules (B)When does it occur? (give answer in cm)

Homework Equations

I have attached a picture of the graph provided on the mastering physics site.
Kmax= (1/2)mv_i_^2

The Attempt at a Solution

Obviously, the mass is provided, but I am not sure how to find the velocity using the graph provided. Or do I simply use an initial velocity of zero? I didn't think using zero velocity was right, however, due to the fact that kinetic energy is only present at the central point in the graph.


Once again, my professor has disabled the "hints" option. Any help offered is appreciated! Thanks in advance!

 

[MaxL]

Start by trying to find the equation of motion of the ball. It'll be of the form x(t) = A*Sin(w*t).

EDIT: Also, you say kinetic energy is only present at the central point in the graph. That's an easy misconception to make. In fact, the ball has kinetic energy at every point in time except where x is at its maximum or minimum. I noticed another strange thing: B) asks "When" but says give the answer in cm. The units don't make sense!

 

[rr263]

For "A" is the equation you are referring to V_i_=sqrt(k/m)x_i_? or is it v_f_=v_i_-WAcos(Wt)? As far as "B" goes, that is what the question asks. I copied the question directly from mastering physics.

 

[MaxL]

The equation I was referring to is the equation for displacement as a function of t--basically, the equation of the line in the graph you posted. I was able to guess its form just by looking at the graph-it's clearly a sine (well, okay, I also know a bit about SHOs, which have equations of motion that are sines and cosines). So my approach would be to find the constants A and w.

From there, you can take the derivative of x(t) with respect to t to get v(t), or alternatively, use w to find the spring constant. Either route can get you to the maximum kinetic energy.

As for part B, that's very strange. Maybe by "when does it occur?" they mean "under what conditions does it occur, in terms of displacement?" You should ask your prof. to clarify that question.

 

[rr263]

Thank you for all your help. I unfortunately wasn't able to check this again before the hmwk was do and wasn't able to figure it out. But thanks anyways!