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Hey, so I am just working on a second year Analytical Mechanics

  1. Oct 18, 2011 #1
    Hey, so I am just working on a second year Analytical Mechanics assignment, and right now dealing with oscillations. I have two questions I am stumped on and don't know if I have it right. It is probably basic, but just checking.

    6. The frequency fd of a damped oscillator is 100 Hz, and the ratio of
    the amplitudes of two successive maxima is one half. What is the
    undamped frequency f0 of this oscillator?

    e-[itex]\gamma[/itex]Td = [itex]\frac{1}{2}[/itex]
    [itex]\gamma[/itex] = [itex]\frac{1}{Td}[/itex]ln 2
    fd ln 2
    [itex]\varpi[/itex]d = ([itex]\varpi[/itex]02 - [itex]\gamma[/itex]2)[itex]\frac{1}{2}[/itex]
    [itex]\varpi[/itex]0 = ([itex]\varpi[/itex]d2 + [itex]\gamma[/itex]2)[itex]\frac{1}{2}[/itex]
    fo = [fd2 + [itex]\frac{\gamma}{2\pi}[/itex]2][itex]\frac{1}{2}[/itex]
    = fd[1+([itex]\frac{ln2}{2\pi}[/itex])2][itex]\frac{1}{2}[/itex]
    fo = 100.6Hz

    Is this correct?

    7. An overdamped harmonic oscillator with ω0 = γ/2 is kicked out of equi-
    librium x(t = 0) = 0 with the initial velocity v0. Find the displacement
    x of the oscillator at time t = (2γ)-1.

    As with this one, I don't know where to begin. Anyone be able to give me a hand starting it?

    Cheers
     
  2. jcsd
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