A body executing a simple harmonic motion has an angular velocity of 22 radians per second. If it has a…

Analyze the question: A body in SHM has angular velocity ω = 22 rad/s and amplitude A = 10 cm. We need its linear velocity. The question doesn't say where in the motion, so it is asking for the maximum linear velocity, which occurs at the equilibrium (centre) position.

Concept: In SHM, the velocity at displacement x is

v = ω√(A² − x²)

At the centre (x = 0), the velocity is greatest:

v_max = ωA

This is the same as the linear speed of the reference circular motion, v = ωr.

Solution:

1. Convert the amplitude to metres: A = 10 cm = 0.10 m
2. Apply v = ωA: v = 22 × 0.10 = 2.2 m/s

Answer: The linear velocity is 2.2 m/s, which is option E.

Tip: Always convert cm to m before substituting. Using 10 instead of 0.1 gives 220 m/s, which is the trap option C. Also remember that "maximum displacement" means amplitude, and that v = ωA is the maximum speed in SHM.