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Q.
A linear harmonic oscillator of force constant $2 \times 10^{6} \,N / m$ times and amplitude $0.01 \,m$ has a total mechanical energy of $160$ joules. Its
Oscillations
Solution:
Harmonic oscillator has some initial elastic potential energy and amplitude of harmonic variation of energy is
$\frac{1}{2} k a^{2}=\frac{1}{2} \times 2 \times 10^{6}(0.01)^{2}=100 \,J$
This is the maximum kinetic energy of the oscillator.
Thus, $K_{\max }=100 \,J$
This energy is added to initial elastic potential energy may give maximum mechanical energy to have value $160 \,J$.