The graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at is [2023]

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Q.
The $x - t$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t = 2$ $s$ is [2023]

1 $\frac{π^{2}}{16} {ms}^{- 2}$

2 $- \frac{π^{2}}{16} {ms}^{- 2}$

3 $\frac{π^{2}}{8} {ms}^{- 2}$

4 $- \frac{π^{2}}{8} {ms}^{- 2}$

Ans.
(2)

Here, $ω = \frac{2 π}{8} = \frac{π}{4} s^{- 1}$

$a = - A ω^{2} = - (1) {(\frac{π}{4})}^{2} = - \frac{π^{2}}{16} {ms}^{- 2}$

Thus, option (2) is correct.

Solution

Q.
The $x - t$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t = 2$ $s$ is [2023]

1 $\frac{π^{2}}{16} {ms}^{- 2}$

2 $- \frac{π^{2}}{16} {ms}^{- 2}$

3 $\frac{π^{2}}{8} {ms}^{- 2}$

4 $- \frac{π^{2}}{8} {ms}^{- 2}$

Ans.
(2)

Here, $ω = \frac{2 π}{8} = \frac{π}{4} s^{- 1}$

$a = - A ω^{2} = - (1) {(\frac{π}{4})}^{2} = - \frac{π^{2}}{16} {ms}^{- 2}$

Thus, option (2) is correct.

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Solution

Q. The x-t graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at t=2s is [2023]

1 π216 ms-2

2 -π216 ms-2

3 π28 ms-2

4 -π28 ms-2

Ans. (2) Here, ω=2π8=π4s-1 a=-Aω2=-(1)(π4)2=-π216ms-2 Thus, option (2) is correct.

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Q.
The $x - t$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t = 2$ $s$ is [2023]

1 $\frac{π^{2}}{16} {ms}^{- 2}$

2 $- \frac{π^{2}}{16} {ms}^{- 2}$

3 $\frac{π^{2}}{8} {ms}^{- 2}$

4 $- \frac{π^{2}}{8} {ms}^{- 2}$

Ans.
(2)

Here, $ω = \frac{2 π}{8} = \frac{π}{4} s^{- 1}$

$a = - A ω^{2} = - (1) {(\frac{π}{4})}^{2} = - \frac{π^{2}}{16} {ms}^{- 2}$

Thus, option (2) is correct.