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Question
The energy of system in simple harmonic motion is given by \[E = \frac{1}{2}m \omega^2 A^2 .\] Which of the following two statements is more appropriate?
(A) The energy is increased because the amplitude is increased.
(B) The amplitude is increased because the energy is increased.
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Solution
Statement A is more appropriate because the energy of a system in simple harmonic motion is given by \[E = \frac{1}{2}m \omega^2 A^2 .\]
If the mass (m) and angular frequency (ω) are made constant, Energy (E) becomes proportional to the square of amplitude (A2).
i.e. E ∝ A2
Therefore, according to the relation, energy increases as the amplitude increases.
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