Question

Position of a \(2\,\text{kg}\) mass moving along the \(x\)-axis is given by \[ x=2\cos[(2\,\text{s}^{-1})t]\ \text{m}. \] Then maximum kinetic energy of the mass in joule is

• A. \(4\)
• B. \(8\)
• C. \(12\)
• D. \(16\)

Hint:

For SHM, \[ v_{\max}=A\omega \] and \[ K_{\max}=\frac{1}{2}mA^2\omega^2. \] Maximum kinetic energy occurs at the mean position.

Answer 1

The Correct Option is D

Step 1: Identify amplitude and angular frequency.
From x = 2cos(2t), amplitude A = 2 m and ω = 2 rad/s.

Step 2: Compute maximum speed.
v_max = Aω = 2 × 2 = 4 m/s.

Step 3: Use kinetic energy formula.
K_max = ½ m v_max² = ½ × 2 × 16 = 16 J.

Step 4: Final Answer:
16 J.