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Simple Harmonic Motion and Maximum Speed

  1. Apr 2, 2007 #1
    1. The problem statement, all variables and given/known data

    An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk (m = 0.08 g) driven back and forth in SHM at 1.5 MHz by an electromagnetic coil.

    (a) The maximum restoring force that can be applied to the disk without breaking it is 34,000 N. What is the maximum oscillation amplitude that won't rupture the disk?

    (b) What is the disk's maximum speed at this amplitude?

    2. Relevant equations

    F = -kx
    w = (2pi)f
    w = (k/m)^.5
    V = wA

    3. The attempt at a solution

    w = (2pi)(1.5E3)
    w = (k/(0.08E-3)^.5 solve for k
    F = -kx solve for x

    I found the amplitude (part a) to be 4.784 micrometers

    Now I am running into problems for part b. I am trying to use V = wA and I get V = 0.0450 m/s, but that answer is not right. Any ideas on what I am doing wrong?

  2. jcsd
  3. Apr 2, 2007 #2
    M is million
  4. Apr 2, 2007 #3
    Thanks! I wonder how I got the first part right. :smile:
  5. Apr 2, 2007 #4
    lol. I was wondering that too.
  6. Apr 3, 2007 #5
    Yeah, lol. Thanks again for your help.
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