First slide

Simple hormonic motion

Question

Maximum velocity of a particle executing SHM is V. Then average speed of the particle over half cycle is

Moderate

A

$\frac{V}{π}$
B

$\frac{2 V}{π}$
C

$\frac{V}{2 π}$
D

$\frac{V}{2}$

Solution

If A be the amplitude and T be the time period of oscillations, then $V_{\max} = A ω$
$∴ A . \frac{2 π}{T} = V \Rightarrow \frac{2 A}{T} = \frac{V}{π}$
$∴$ Average speed over half cycle
$= \frac{2 A}{T / 2} = 2 (\frac{2 A}{T}) = \frac{2 V}{π}$

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