Question

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 from equilibrium position to half of its amplitude.

• A. 4 cm/s
• B. 6 cm/s
• C. 12 cm/s
• D. 16 cm/s

Answer 1

Answer: (C)

Given: Time period, T = 0.5 sec
Amplitude, $A=1cm$
Average velocity in the interval in which body moves from equilibrium to half of its amplitude, v = ?
Time taken to a displacement A/2 where A is the amplitude of oscillation from the mean position ‘O’ is $\frac{T}{12}$
Therefore, time, $t=\frac{0.5}{12}sec$
Displacement, $s=\frac{A}{2}=\frac{1}{2}cm$
$\therefore$ Average velocity, $v=\frac{\frac{A}{2}}{t}=\frac{\frac{1}{2}}{\frac{0.5}{12}}=12cm/s$