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For a particle executing SHM, the displa...

For a particle executing SHM, the displacement `x` is given by `x = A cos omegat`. Identify the graph which represents the variation of potential energy `(PE)` as a function of time `t` and displacement `x`.

(a) `I, III`
(b) `II, IV` (c ) `II, III`
(d) `I, IV`

Text Solution

Verified by Experts

The correct Answer is:
A
Potential energy is minimum (in this case zero) at mean position `(x = 0)` and maximum at extreme positions `(x = + A)`.
At time `t = o`, `x = A`. Hence, `PE` should be maximum. Therefore, graph `I` is correct. Furhter in graph III, `PE` is minimum at `x = 0`. Hence, this is also correct.
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Knowledge Check

  • For a particle executing S.H.M. the displacement x is given by x= A cos omegat . Identify the graph which represents the variation of potential energy (P.E.) as a function of time

    A
    I,III
    B
    II, IV
    C
    II, III
    D
    I,IV

  • For a particle executing SHM , the kinetic energy (K) is given by K = K_(0)cos^(2) omegat . The equation for its displacement is

    A
    `((K_(0))/(m omega^(2)))^((1)/(2)) sin omegat`
    B
    `((2K_(0))/(m omega^(2)))^((1)/(2)) sin omegat`
    C
    `((2omega^(2))/(m K_(0)))^((1)/(2)) sin omegat`
    D
    `((2K_(0))/(m omega^(2)))^((1)/(2)) sin omegat`

  • The displacement of a particle is given by x = cos^(2) omegat. The motion is

    A
    simple harmonic
    B
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    C
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    D
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