First slide

Simple harmonic motion

Question

A body of mass 5 g is executing SHM about a fixed point, with amplitude of 10 cm and maximum velocity 100 cm s^–1. Its velocity will be 50 cm s^–1at a distance of

Moderate

A

5 cm
B

$5 \sqrt{2} cm$
C

$5 \sqrt{3} cm$
D

$10 \sqrt{2} cm$

Solution

$\begin{array}{l} V_{max} = 100 {cms}^{- 1} \\ i.e., A ω = 100 \\ ∴ ω = \frac{100}{A} = \frac{100}{10} = 10 rad / s \\ Now, v^{2} = ω^{2} (A^{2} - y^{2}) \\ 50^{2} = 10^{2} (10^{2} - y^{2}) \\ y = \sqrt{75} = 5 \sqrt{3} cm . \end{array}$

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