The total mechanical energy of a spring-mass | vedclass

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(D) The total mechanical energy of a spring-mass system is given by $E = \frac{1}{2}kA^2$,where $k$ is the spring constant and $A$ is the amplitude.We

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remain same

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(D) The total mechanical energy of a spring-mass system is given by $E = \frac{1}{2}kA^2$,where $k$ is the spring constant and $A$ is the amplitude.We know that for a spring-mass system,the angular frequency is $\omega = \sqrt{\frac{k}{m}}$,which implies $k = m\omega^2$.Substituting $k = m\omega^2$ into the energy equation,we get $E = \frac{1}{2}(m\omega^2)A^2$.When the mass $m$ is replaced by $2m$,the spring constant $k$ of the spring remains unchanged because the spring itself is not replaced.Since the total mechanical energy $E = \frac{1}{2}kA^2$ depends only on the spring constant $k$ and the amplitude $A$,and both $k$ and $A$ remain constant,the total mechanical energy $E$ remains the same.

The total mechanical energy of a spring-mass system in simple harmonic motion is $E = \frac{1}{2}m\omega^2 A^2$. Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude $A$ remains the same. The new mechanical energy will:

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