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Simple Harmonic Motion

  1. Feb 20, 2013 #1
    1. The problem statement, all variables and given/known data
    A massless spring hangs down from a support, with its lower end at y=0, where the y-axis is vertical and points downward (normal orientation of y). When a small unknown mass is attached to the spring, the lower end of the spring moves down to a position y_0 for the mass being in equilibrium

    a.) Demonstrate that when the mass is pulled down to a position of y=y_0 + A and released from rest, it will execute a simple harmonic motion around y_0

    b.) Express the period of oscillations of the mass in terms of y_0 and g.

    2. Relevant equations

    3. The attempt at a solution

    Not really sure what/how to demonstrate that it executes s.h.m. I set up a force equation such that F_net= F_restoring - mg

    F_net= -k(y-y_0) - mg
    let Y be acceleration
    mY= -k(y-y_0) - mg

    mY=-kA-mg definfe ω^2 = k/m

    Y=-(ω^2)A - g is the final equation i got... not sure how this proves anything and not really sure what to do.. any help? thanks
  2. jcsd
  3. Feb 21, 2013 #2

    Simon Bridge

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    Science Advisor
    Homework Helper

    Start with the definition of SHM.
    Good start - how is the force related to displacement? Use words - and relate it to the definition of SHM.
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