First slide

Simple harmonic motion

Question

The x-t graph of a particle undergoing simple harmonic motion is shown below. The velocity of the particle at t = $\frac{4}{3} \sec$ is

Moderate

A

$\frac{π}{8} c m / s$
B

$\frac{- π}{8} c m / s$
C

$\frac{π^{2}}{32} c m / s$
D

$\frac{- \sqrt{3}}{32} π^{2} c m / s$

Solution

From the graph, time period, T = 8 sec.
Equation of motion is
$\begin{array}{l} x (cm) = (1 cm) \sin (\frac{2 π}{8} t) \\ v = \frac{π}{4} \cos (\frac{π}{4} t) \\ At t = \frac{4}{3} \sec, v = \frac{π}{4} \cos (\frac{π}{4} \frac{4}{3}) = \frac{π}{8} cm / s . \end{array}$

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