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(A) The total energy $E$ of a particle executing simple harmonic motion $(SHM)$ is given by the formula:$E = \frac{1}{2} m \omega^2 A^2$where $m$ is t

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$(1)$ and $(2)$ are correct

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(A) The total energy $E$ of a particle executing simple harmonic motion $(SHM)$ is given by the formula:$E = \frac{1}{2} m \omega^2 A^2$where $m$ is the mass of the particle,$\omega$ is the angular frequency,and $A$ is the amplitude.Since $\omega = \frac{2\pi}{T}$,where $T$ is the period,we can substitute this into the energy equation:$E = \frac{1}{2} m \left( \frac{2\pi}{T} \right)^2 A^2 = \frac{2 \pi^2 m A^2}{T^2}$From this expression,it is clear that the total energy $E$ depends on the amplitude $A$ and the period $T$.The total energy in $SHM$ is constant at all points in time and does not depend on the instantaneous displacement $x$.Therefore,statements $(1)$ and $(2)$ are correct.

Consider the following statements. The total energy of a particle executing simple harmonic motion depends on its:
$(1)$ Amplitude $(2)$ Period $(3)$ Displacement
Of these statements:

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Consider the following statements. The total energy of a particle executing simple harmonic motion depends on its:$(1)$ Amplitude $(2)$ Period $(3)$ DisplacementOf these statements: