A linear harmonic oscillator of force constant $2 \times 10^{6} {Nm}^{- 1}$ and amplitude 0.01 m has a total mechanical energy 160 J. Among the following statements, which are correct?
i. Maximum PE is 100 J
ii. Maximum KE is 100 J
iii. Maximum PE is 160 J
iv. Minimum PE is zero

Question

A linear harmonic oscillator of force constant $2 \times 10^{6} {Nm}^{- 1}$ and amplitude 0.01 m has a total mechanical energy 160 J. Among the following statements, which are correct?

i. Maximum PE is 100 J
ii. Maximum KE is 100 J
iii. Maximum PE is 160 J
iv. Minimum PE is zero

Infinity Learn · Accepted Answer

Total mechanical energy is ET $$=$$ $$160$$ J ∴  Umax $$=$$ $$160$$ JAt extreme position $$KE$$ is zero. Work done by spring force from extreme position to mean position isW $$=$$ $$12kA2$$∴  Kmax $$=$$ W $$=$$ $$12(2$$×$$106)(0.01)2$$ $$=$$ $$100$$ J∴  $$Umin=$$ $$160-100$$ $$=$$ $$60$$ J

A linear harmonic oscillator of force constant $2 \times 10^{6} {Nm}^{- 1}$ and amplitude 0.01 m has a total mechanical energy 160 J. Among the following statements, which are correct?
i. Maximum PE is 100 J
ii. Maximum KE is 100 J
iii. Maximum PE is 160 J
iv. Minimum PE is zero

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A linear harmonic oscillator of force constant 2×106 Nm-1and amplitude 0.01 m has a total mechanical energy 160 J. Among the following statements, which are correct?i. Maximum PE is 100 Jii. Maximum KE is 100 Jiii. Maximum PE is 160 Jiv. Minimum PE is zero

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Ready to Test Your Skills?

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A linear harmonic oscillator of force constant $2 \times 10^{6} {Nm}^{- 1}$ and amplitude 0.01 m has a total mechanical energy 160 J. Among the following statements, which are correct?
i. Maximum PE is 100 J
ii. Maximum KE is 100 J
iii. Maximum PE is 160 J
iv. Minimum PE is zero