1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Oscillation Frequency, Total Mechanical Energy, and Initial Speed

  1. Dec 8, 2009 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant 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

    3. 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.
    Last edited: Dec 8, 2009
  2. jcsd
  3. Dec 8, 2009 #2
    I am confused! Why did you calculate k while it is given in the picture?
  4. Dec 8, 2009 #3
    How is K given in the picture? Am I missing something? Which is totally possible. Is the 20 N/m the spring constant?
  5. Dec 8, 2009 #4
    You can figure it out by determining its dimension :)
  6. Dec 8, 2009 #5
    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!
  7. Dec 8, 2009 #6
    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....
  8. Dec 8, 2009 #7
    you have 2 eq.:

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

    let t = 0 :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook