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Explain the relation in phase between di...

Explain the relation in phase between displacement velocity and acceleration in SHM, graphically as well as theoretically.

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The relation in phase between displacement, velocity and acceleration in SHM can be shown graphically.
Displacement `x=Asin(omegat+phi_(0))`.

Velocity, `v=omegaAcos(omegat+phi_(0))`

Acceleration `a=-omega^(2)Asin(omegat+phi_(0))`

Here, x and v differ in phase by `pi/2`, v and a differ in phase by `pi/2`.
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Knowledge Check

  • In SHM, displacement, velocity and acceleration all oscillate simple harmonically with same angular frequency omega . Phase difference between any two is pi/2 except that between displacement and acceleration which is pi Displacement time equation of a particle is given as, x=Asin(omegat+pi/6)-Acos (omegat+pi/2)

    A
    The motion of the particle is not simple harmonic
    B
    at t=0, acceleration of particle is positive
    C
    at t=0, velocity is negative
    D
    none of above

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