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Show that y=sin^(2)omegat does not repre...

Show that `y=sin^(2)omegat` does not represent simple harmonic but periodic. What is the period of the given function.

Text Solution

Verified by Experts

Given, `y=sin^(2)omegat` or `y=(1)/(2)(1-cos 2omegat)`
Velocity of the particle `v=(dy)/(dx)=(1)/(2)[0+(sin2omegat)(2omega)]`
`v=(omega)sin2omegat`
Particle acceleration `a=(dv)/(dt)=2omega^(2)cos2omega t`
Hence `y=sin^(2)omegat` is periodic but does not execute S.H.M. Acceleration is not proportional to the displacement.
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Knowledge Check

  • The function sin^(2)(omegat) represents :

    A
    a periodic, but not simple harmonic motion with a period `2pi//omega`
    B
    a periodic, but not simple harmonic motion with a period `pi//omega`
    C
    a simple harmonic motion with a period `2pi//omega`
    D
    a simple harmonic motion with a period `pi//omega`

  • If f(x) is an odd periodic function with period 2 then f(4)=

    A
    0
    B
    2
    C
    4
    D
    -4

  • The period of the function y=|sinx|+|cosx| is :

    A
    `pi`
    B
    `4pi`
    C
    `pi//2`
    D
    `2pi`

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