Oscillation Frequency, Total Mechanical Energy, and Initial Speed

[KatlynEdwards]

Homework Statement

The figure shows a block on a frictionless surface attached to a spring. The block is pulled out to position x_i = 20 cm, then given a "kick" so that it moves to the right with speed v_i. The block then oscillates with an amplitude of 44 cm.

Image of the problem - http://session.masteringphysics.com/problemAsset/1013861/11/jfk.Figure.Q14.21.jpg

What is the oscillation frequency?

What is the total mechanical energy of the oscillator?

What was the initial speed v_i?

Homework Equations

Hooke's Law
Force = k*change in distance

Frequency - (1/2*pi)*sqrt(k/mass)

Total mechanical energy = potential energy + kinetic energy

Potential energy = 1/2*k*Amplitude^2

Kinetic energy = 1/2 * mass*v_max^2

The Attempt at a Solution

F=k*change in x
20 = k*0.2
k = 100

Frequency= (1/2pi) * sqrt(k/m)
Frequency=(1/2pi) * sqrt (100/.5)
Frequency=2.251 Hz

For some reason the answer is 1.0 Hz but I can't figure out what I did wrong. Once I figure this one out I can move onto the next two.

 

[ApexOfDE]

I am confused! Why did you calculate k while it is given in the picture?

 

[KatlynEdwards]

How is K given in the picture? Am I missing something? Which is totally possible. Is the 20 N/m the spring constant?

 

[ApexOfDE]

You can figure it out by determining its dimension :)

 

[KatlynEdwards]

Yeah you were right. The spring constant was in fact labeled in the picture xD. I feel rather stupid now, especially since that was the only thing wrong :P. Oh well. Lesson learned - look at ALL the information. Haha. Thanks for the help!

 

[KatlynEdwards]

Okay so I figured out the first part, and the second part (1.936) but now I'm stuck on the third part - finding the initial speed. I know that I should use v(t)=-vmax*sin(2*pi*frequency*t) but we don't know t. And a t of zero gives me an answer of zero...

 

[ApexOfDE]

you have 2 eq.:

x = A * cos(wt + phi)
v = vm * sin(wt + phi)

let t = 0 :)