A particle of mass 4 ,kg is executing SHM. It | vedclass

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(A) The equation of motion for the particle is given by $y = 8 \cos [100 t + \pi / 4] \,cm$.Comparing this with the standard $SHM$ equation $y = a \co

Vedclass · Accepted Answer

$128$

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(A) The equation of motion for the particle is given by $y = 8 \cos [100 t + \pi / 4] \,cm$.Comparing this with the standard $SHM$ equation $y = a \cos(\omega t + \phi)$, we get:Amplitude $a = 8 \,cm = 8 	imes 10^{-2} \,m$Angular frequency $\omega = 100 \,rad/s$Mass $m = 4 \,kg$The maximum kinetic energy $(K_{max})$ in $SHM$ is given by the formula:$K_{max} = \frac{1}{2} m \omega^2 a^2$Substituting the values:$K_{max} = \frac{1}{2} 	imes 4 	imes (100)^2 	imes (8 	imes 10^{-2})^2$$K_{max} = 2 	imes 10000 	imes 64 	imes 10^{-4}$$K_{max} = 2 	imes 10000 	imes 0.0064$$K_{max} = 128 \,J$

$A$ particle of mass $4 \,kg$ is executing $SHM$. Its displacement is given by the equation $y=8 \cos [100 t+\pi / 4] \,cm$. Its maximum kinetic energy is (in $\,J$)

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