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For a particle performing S.H.M along $x$ axis, position $(x)$ and time (t) are as shown
Acceleration of particle at t = 2s is ____ $cm / s^{2}$ $(Take π^{2} ≃ 10)$

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$6.25$

$- 6.25$

$12.5$

$- 12.5$

answer is B.

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Detailed Solution

1) T = 8s

$ω = \frac{2 π}{T} = \frac{2 π}{8} = \frac{π}{4} rad / sec$

2) $a_{t = 2s} = - ω^{2} x_{t= 2 s}$

$= - \frac{π^{2}}{16} (0.2) m / s^{2}$

$= - \frac{10}{16} (0.2) (100) cm / s^{2}$

$= - 12.5 cm / s^{2}$

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