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(B) The total mechanical energy $(T.E.)$ of a simple harmonic oscillator is given by the formula:$T.E. = \frac{1}{2} k A^2$where $k$ is the force cons

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$E$

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(B) The total mechanical energy $(T.E.)$ of a simple harmonic oscillator is given by the formula:$T.E. = \frac{1}{2} k A^2$where $k$ is the force constant of the spring and $A$ is the amplitude of oscillation.From the formula,it is clear that the total energy depends only on the force constant $k$ and the amplitude $A$.It does not depend on the mass $m$ of the oscillating particle.Since the amplitude $A$ remains the same and the force constant $k$ (which depends on the spring properties) remains unchanged,the total energy of the system will remain $E$.Therefore,the correct option is $B$.

In simple harmonic motion,the total mechanical energy of a given system is $E$. If the mass of the oscillating particle $P$ is doubled,then the new energy of the system for the same amplitude is

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