Energy of Simple Harmonic Oscillator – Rankers Physics

Energy in SHM: Practice Problem & Solution

Assertion (A): If the amplitude of a simple harmonic oscillator is doubled, its total energy also becomes doubled. Reason (R): In harmonic oscillation, the total energy is directly proportional to the amplitude of vibration.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Energy in SHM. Understanding the underlying formula is key to arriving at the correct answer below:

The total energy of an SHM is `\(E = \frac{1}{2}kA^2\)`. If amplitude `\(A\)` is doubled, energy becomes `\(E' = \frac{1}{2}k(2A)^2 = 4E\)`. So A is false.
Reason R states energy is directly proportional to amplitude, which is also false (it's proportional to `\(A^2\)`). Both are false.

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