The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at is [2009]

Question

The $x - t$ graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t = \frac{4}{3} s$ is [2009]

Smart Achievers · Accepted Answer

(4)

$The equation for the S.H.M. x = a \sin ω t$

$\Rightarrow x = a \sin (\frac{2 π}{T} \times t) = 1 \sin (\frac{2 π}{8}) t = \sin \frac{π}{4} t$ $(∵ a = 1 cm, T = 8 s from graph)$

or, velocity, $v = \frac{d x}{d t} = \frac{d}{d t} [\sin (\frac{π}{4}) t] = \frac{π}{4} \cos (\frac{π}{4}) t$

$∴$ $Acceleration a = \frac{d^{2} x}{d t^{2}} = - {(\frac{π}{4})}^{2} \sin (\frac{π}{4}) t$

At $t = \frac{4}{3} s$ acceleration

$a = \frac{d^{2} x}{d t^{2}} = - {(\frac{π}{4})}^{2} \sin (\frac{π}{4} \times \frac{4}{3})$

$= \frac{- π^{2}}{16} \sin \frac{π}{3}$

$= \frac{- \sqrt{3} π^{2}}{32} {cm/s}^{2}$

Solution

Q.
The $x - t$ graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t = \frac{4}{3} s$ is [2009]

1 $\frac{\sqrt{3}}{32} π^{2} {cm/s}^{2}$

2 $- \frac{π^{2}}{32} {cm/s}^{2}$

3 $\frac{π^{2}}{32} {cm/s}^{2}$

4 $- \frac{\sqrt{3}}{32} π^{2} {cm/s}^{2}$

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Solution

Q. The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t=43 s is [2009]

1 332π2 cm/s2

2 -π232 cm/s2

3 π232 cm/s2

4 -332π2 cm/s2