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  4. 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.

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Q. 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.

JEE MainJEE Main 2014Oscillations

Solution:

Given: Time period, T = 0.5 sec
Amplitude, $A = 1\, cm$
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, $v = \frac{\frac{A}{2}}{t} = \frac{\frac{1}{2}}{\frac{0.5}{12}} = 12\,cm/s$