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17 January, 18:16

For the simple harmonic motion equation d=8 sin (4 pi t), what is the period? If necessary, use the slash (/) to represent a fraction

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  1. 17 January, 20:18
    0
    I assume your question amounts to finding the period of f (t) = 8sin (4 pi t). A period L is a positive number such that f (t+L) = f (t) for all t. Since sin (x) is 2 pi perodic we can find the least number L such that 4pi (t+L) = 4*pi*t+2*pi. Multiplying out we get

    4pi (t+L) = 4*pi*t+4*pi*L and we want to find L such that we get 4*pi*t+2*pi, notice if we take L=1/2 we get the desiered result 4*pi*t+4*pi*1/2=4*pi*t+2*pi. This proves that L=1/2 and your function has a period of 1/2.
  2. 17 January, 20:33
    0
    D=asin (wt)

    w=2 pi/T

    T=2 pi/w

    T=2 pi/4 pi

    T=1/2
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