Question:

A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is:

38π

4π/3

8π/3

73π

We know that velocity in S. H. M. is given by
v = ω√(a² - x²)
v = ω√(5² - 4²) = 3ω
a = ω²x
Given |a| = |v|
4ω² = 3ω
ω = 3/4
T = 2π/ω = 8π/3 sec.