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13 February, 18:39

An object-spring system undergoes simple harmonic motion with an amplitude A. Does the total energy change if the mass is doubled but the amplitude isn't changed (T/F)

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  1. 13 February, 20:42
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    Answer: No, The energy will remain the same

    Explanation: Doubling the mass and leaving the amplitude unchanged won't have any effect on the total energy of the system.

    At maximum displacement, E=0.5kA^2

    Where E = total energy

    K = spring constant

    A = Amplitude

    From the formula above : Total Energy is independent of mass,. Therefore, total energy won't be affected by Doubling the mass value of the object.

    Also when the object is at a displacement 'x' from its equilibrium position.

    E = Potential Energy (P. E) + Kinetic Energy (K. E)

    P. E = 0.5kx^2

    Where x = displacement from equilibrium position

    E = Total Energy

    K. E = E-0.5kx^2

    From the relation above, total energy is independent of its mass and therefore has no effect on the total energy.
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