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In a simple harmonic motion, the force a...

In a simple harmonic motion, the force acting on a particle is given as `F  = -4x`, total mechanical energy of the particle is 10J and amplitude of oscillation is 2m. At time t = 0 acceleration of the particle is `-16m//s^2`. Mass of the particle is 0.5 kg. 
Potential energy of the particle at mean position is : 

A

`10 J`

B

`8 J`

C

`6 J`

D

`2 J`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • In a simple harmonic motion, the force acting on a particle is given as F = -4x , total mechanical energy of the particle is 10J and amplitude of oscillation is 2m. At time t = 0 acceleration of the particle is -16m//s^2 . Mass of the particle is 0.5 kg. Displacement time equation of the particle is:

    A
    `x = 2 sin 2 t`
    B
    `x = 2 sin 4 t`
    C
    `x = 2 cos 2 t`
    D
    `x = 2 cos (2 sqrt(2) t)`

  • In a simple harmonic motion, the force acting on a particle is given as F = -4x , total mechanical energy of the particle is 10J and amplitude of oscillation is 2m. At time t = 0 acceleration of the particle is -16m//s^2 . Mass of the particle is 0.5 kg. At x = +1m, potential energy and kinetic energy of the particle are

    A
    `2 J and 8 J`
    B
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    D
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  • The total energy of a particle executing simple harmonic motion is:

    A
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    C
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    D
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