An object of mass 0.2 ,kg executes simple har | vedclass

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(C) The total energy $(E)$ of an object in simple harmonic motion is the sum of its kinetic energy $(K.E.)$ and potential energy $(P.E.)$.$E = K.E. +

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(C) The total energy $(E)$ of an object in simple harmonic motion is the sum of its kinetic energy $(K.E.)$ and potential energy $(P.E.)$.$E = K.E. + P.E. = 0.5 \,J + 0.4 \,J = 0.9 \,J$.The total energy is also given by the formula $E = \frac{1}{2} m \omega^2 A^2$, where $m$ is the mass, $\omega$ is the angular frequency, and $A$ is the amplitude.The angular frequency $\omega = 2 \pi f = 2 \pi 	imes (\frac{25}{\pi}) = 50 \,rad/s$.Substituting the values: $0.9 = \frac{1}{2} 	imes 0.2 	imes (50)^2 	imes A^2$.$0.9 = 0.1 	imes 2500 	imes A^2$.$0.9 = 250 	imes A^2$.$A^2 = \frac{0.9}{250} = 0.0036 \,m^2$.$A = \sqrt{0.0036} = 0.06 \,m$.Converting to centimeters: $A = 0.06 	imes 100 = 6 \,cm$.

An object of mass $0.2 \,kg$ executes simple harmonic motion along the $x$-axis with a frequency of $(\frac{25}{\pi}) \,Hz$. At the position $x=0.04 \,m$, the object has a kinetic energy of $0.5 \,J$ and a potential energy of $0.4 \,J$. The amplitude of oscillation is ............ $cm$.

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