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Trig question (sine wave)

  1. Jun 2, 2009 #1
    A piston in a large factory engine moves up and down in a cylinder. The height, h centimeters, of the piston at t seconds is given by the formula h = 120sinPi(t)+200.

    a) State the amplitude and period.
    b) What are the maximum and minimum heights of the piston?
    c) How many complete cycles does the piston make in 30 min?

    My answers:

    ai) amplitude = 120cm
    aii) period = 2Pi / Pi = 2

    bi) minimum height = 200cm - 120cm = 80cm
    bii) maximum height = 200cm + 120cm = 320cm

    c) 30m = 1800s
    period = 2 cycles / s
    1800 x 2 = 3600

    Therefore the piston makes 3600 complete cycles in 30 minutes.

    I was hoping that someone could tell me if my answers are correct? I want to make sure that I understand this properly. Thanks :)
     
  2. jcsd
  3. Jun 2, 2009 #2

    cepheid

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    Part c looks wrong. The period is 2 seconds, which corresponds to half a cycle per second. You know that if it takes *longer* than one second to go through a complete cycle, then you will able to go through *fewer* than 1800 full cycles in 1800 seconds.
     
  4. Jun 2, 2009 #3
    Oops sorry about that I typed it in wrong :(

    I meant the following:

    c) 30m = 1800s
    period = 2
    1800s / 2 = 900

    Therefore the piston makes 900 complete cycles in 30 minutes. Thanks for pointing that out.
     
  5. Jun 2, 2009 #4

    cepheid

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    No problem. Everything else looks good to me.
     
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