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Spring Problem

  1. Dec 16, 2003 #1
    This was a problem on my final exam that I couldn't figure out, it drove me insane. Someone please tell me it's impossible :wink:

    A spring has a 1kg block attached to it and a k of 30,000. A 2kg block moving at 30m/s over a frictionless surface hits and sticks to the 1kg block. What is the displacement of the spring? What frequency will it vibrate after impact?

    I figured out that the final velocity of both blocks will be 20m/s and the final mass will be 3kg. I could not figure out the final acceleration to use m*a=x*k

    I was not given the distance between the blocks or the time.

    Any ideas?
  2. jcsd
  3. Dec 16, 2003 #2


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    Step 1) What is the kinetic energy of the resulting 3 kg lump?

    Step 2) The work done by the lump in compressing the spring can be found by

    W = \int F\, dx
    = \int kx\, dx
    = \frac{1}{2} kx^2

    where W is equal to the kinetic energy of the lump.

    The angular velocity of oscillation of a system with "springiness" k and mass m is

    [tex]\omega = \sqrt{\frac{k}{m}[/tex]

    The frequency of an oscillation with angular velocity [itex]\omega[/itex] is

    [tex]f = \frac{\omega}{2 \pi}[/tex]

    Does this make sense?

    - Warren
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