A particle executes SHM with amplitude 5 cm. At displacement 4 cm from the mean position, the numerical value of its velocity in SI units equals that of its acceleration. Find the period.
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Question

A particle executes SHM with amplitude 5 cm. At displacement 4 cm from the mean position, the numerical value of its velocity in SI units equals that of its acceleration. Find the period.

G1 Physics · Accepted Answer

At x=4 cm with amplitude 5 cm, v=ω√(5²−4²) cm s⁻¹=3ω cm s⁻¹=0.03ω m s⁻¹. Acceleration magnitude is ω²x=0.04ω² m s⁻². Numerical equality gives 0.03ω=0.04ω², so ω=0.75 rad s⁻¹. Hence T=2π/0.75=8π/3 s. Correct option: 4.