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Oscillations — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsOscillations3 Marks
Question
For a particle performing linear SHM, show that its average speed over one oscillation is $\frac{2 \omega A}{\pi}$, where $A$ is the amplitude of SHM.
OR
Show that the average speed of a particle performing SHM in one oscillation is $\frac{2}{\pi} \times$ maximum speed.
✓

Answer


During one oscillation, a particle performing SHM covers a total distance equal to $4 A$, where A is the amplitude of SHM. The time taken to cover this distance is the period (T) of SHM.
$
\text { Average speed }=\frac{\text { distance covered } \text { in one oscillation }}{\text { time taken for one oscillation }}
$
$
\therefore v_{ av }=\frac{4 A }{T} \quad
$
But $T=\frac{2 \pi}{\omega}$
where $\omega$ is a constant related to the system.
$
\therefore v_{a v}=4 A \times \frac{\omega}{2 \pi}=\frac{2 \omega A}{\pi}
$
But $\omega A=$ maximum speed
$
\therefore \text { Average speed }=\frac{2}{\pi} \times \text { maximum speed }
$

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