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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.
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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