Question

A particle executes linear simple harmonic motion and its potential energy (P.E.), kinetic energy (K.E.), total energy (T.E.) are measured as functions of displacement \(x\) from the mean position at the origin. Then

• A. K.E. is minimum when \(x = 0\)
• B. T.E. is zero when \(x = 0\)
• C. P.E. is maximum when \(x = 0\)
• D. K.E. is maximum when \(x\) is maximum
• E. P.E. is maximum when \(x\) is maximum

Hint:

In SHM: KE max at mean, PE max at extremes.

Answer 1

Answer: (E)

Concept: In SHM: \[ PE = \frac{1}{2}kx^2 \]

Step 1: At mean position (\(x=0\)).
\[ PE = 0,\quad KE = \text{maximum} \]

Step 2: At extreme position.
\[ x = \text{maximum} \Rightarrow PE = \text{maximum},\quad KE = 0 \]