A body is in simple harmonic motion with time period half second \((T\, = 0.5\, s)\) and amplitude one \(cm\, (A\,= 1\, cm)\). Find the average velocity in the interval in which it moves form equilibrium position to half of its amplitude .... \(cm/s\)

Amplitude, \(\mathrm{A}=1 \mathrm{cm}\)

Average velocity in the interval in which body moves from equilibrium to half of its amplitude, \(\mathrm{v}=?\)

Time taken to a displacement \(A/2\) where \(A\) is the amplitude of oscillation from the

mean position \(^{\prime} \mathrm{O}^{\prime}\) is \(\frac{\mathrm{T}}{12}\)

Therefore, time, \(t=\frac{0.5}{12} \mathrm{sec}\)

Displacement, \(s=\frac{A}{2}=\frac{1}{2} c m\)

Average velocity, \(v=\frac{\frac{A}{2}}{t}=\frac{\frac{1}{2}}{\frac{0.5}{12}}=12 \mathrm{cm} / \mathrm{s}\)