The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t =43sec is

A
$\frac{\sqrt{3}}{32} π^{2} c m / s^{2}$
B
$\frac{- π^{2}}{32} c m / s^{2}$
C
$\frac{π^{2}}{32} c m / s^{2}$
D
$\frac{- \sqrt{3}}{32} π^{2} c m / s^{2}$

Solution:

From the graph, time period, T = 8 sec.
Equation of motion is
$\begin{array}{l} x (cm) = (1 cm) \sin (\frac{2 π}{8} t) \\ v = \frac{π}{4} \cos (\frac{π}{4} t) \\ a = - {(\frac{π}{4})}^{2} \sin (\frac{π}{4} t) \\ At t = \frac{4}{3} \sec, a = - (\frac{π^{2}}{16}) \sin (\frac{π}{4} \frac{4}{3}) = - \frac{\sqrt{3}}{32} π^{2} cm / s^{2} . \end{array}$

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

Solution:

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