Question

If the amplitude of linear S.H.M. is decreased then

• A. its period and total energy will increase.
• B. its period will increase and total energy will decrease.
• C. its period and total energy will decrease.
• D. its period will not change but total energy will decrease.

Hint:

Remember that the absolute definition of harmonicity means that the frequency and period are amplitude-independent properties (isochronism). Thus, you can immediately eliminate options (A), (B), and (C) during an exam without doing any math, as they all incorrectly predict a change in the period!

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Apply the defining property of simple harmonic motion—isochronism—to eliminate incorrect options about period dependence.

Step 2: Key Formula or Approach:
A fundamental characteristic of SHM is that the period (and frequency) is completely independent of the amplitude. This isochronous nature means changing the amplitude cannot alter the period.

Step 3: Detailed Explanation:
Options (A), (B), and (C) all predict some change in the period—whether increasing, decreasing, or becoming amplitude-dependent. Since true harmonic motion has an amplitude-invariant period by definition, all three can be eliminated on conceptual grounds alone, without any mathematical computation. This principle-based elimination is the fastest route to the correct answer.

Step 4: Final Answer:
The period remains unchanged regardless of amplitude, ruling out options predicting any change.