An object of mass 3 ,kg is executing simple h | vedclass

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(B) Given: Mass $m = 3 \,kg$, Amplitude $A = \frac{2}{\pi} \,m$, Kinetic energy at mean position $K_{max} = 6 \,J$. At the mean position, the kinetic

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(B) Given: Mass $m = 3 \,kg$, Amplitude $A = \frac{2}{\pi} \,m$, Kinetic energy at mean position $K_{max} = 6 \,J$. At the mean position, the kinetic energy is equal to the total energy of the simple harmonic oscillator: $K_{max} = \frac{1}{2} m \omega^2 A^2 = 6 \,J$. Substituting $\omega = \frac{2\pi}{T}$, we get: $\frac{1}{2} m (\frac{2\pi}{T})^2 A^2 = 6$. $\frac{1}{2} 	imes 3 	imes \frac{4\pi^2}{T^2} 	imes (\frac{2}{\pi})^2 = 6$. $\frac{1}{2} 	imes 3 	imes \frac{4\pi^2}{T^2} 	imes \frac{4}{\pi^2} = 6$. $6 	imes \frac{4}{T^2} = 6$. $T^2 = 4$, which gives $T = 2 \,s$.

An object of mass $3 \,kg$ is executing simple harmonic motion with an amplitude $\frac{2}{\pi} \,m$. If the kinetic energy of the object when it crosses the mean position is $6 \,J$, the time period of oscillation of the object is (in $\,s$)

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