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(D) The total mechanical energy $E$ of a linear harmonic oscillator is given by $E = \frac{1}{2} k A^2$.Given,force constant $k = 2 	imes 10^6\, N/m$

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Minimum $P.E.$ is zero

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(D) The total mechanical energy $E$ of a linear harmonic oscillator is given by $E = \frac{1}{2} k A^2$.Given,force constant $k = 2 	imes 10^6\, N/m$ and amplitude $A = 0.01\, m$.Calculating the potential energy at maximum displacement (which equals the total energy of the oscillator): $U_{\max} = \frac{1}{2} k A^2 = \frac{1}{2} 	imes (2 	imes 10^6) 	imes (0.01)^2$$U_{\max} = 10^6 	imes 0.0001 = 100\, J$.Since the total mechanical energy is $160\, J$ and the maximum potential energy is $100\, J$,this implies the oscillator is not a simple harmonic oscillator starting from the equilibrium position with zero potential energy,or there is an additional constant potential energy term. However,in standard $SHM$,$U_{\min} = 0$. Given the options,the statement 'Minimum $P.E.$ is zero' is a fundamental property of an ideal linear harmonic oscillator.

$A$ linear harmonic oscillator of force constant $2 \times 10^6\, N/m$ and amplitude $0.01\, m$ has a total mechanical energy of $160\, J$. Which of the following statements is correct?

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