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: ![image](https://pub-7faa453bd1ec4bf0a04cc031c6f058de.r2.dev/images/b001d5da-b5ff-4457-aab2-41651540b290.png)

[Image showing displacement and acceleration graphs in SHM]From the graph, time period T = 8 s and amplitude A = 1 m .Angular frequency ω = 2π/T = 2π/8 = π/4 rad/s .Acceleration a = -ω^2 x .At t = 2 s , the particle is at x = A (ω t) = 1 ≤ft(π/4 × 2) = ≤ft(π/2) = 1 m . a = -≤ft(π/4)^2 × 1 = -π^2/16 m/s^2

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: ![image](https:/ - Physics MCQ NEET 2023 2026 | ExamTest.live

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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:

A $\frac{π ^{2}}{8} m s^{- 2}$
B $- \frac{π ^{2}}{8} m s^{- 2}$
C $\frac{π ^{2}}{16} m s^{- 2}$
D $- \frac{π ^{2}}{16} m s^{- 2}$

Solution & Step-by-step Explanation

[Image showing displacement and acceleration graphs in SHM]From the graph, time period T = 8 s and amplitude A = 1 m .Angular frequency ω = \frac{2 π}{T} = \frac{2 π}{8} = \frac{π}{4} rad/s .Acceleration a = - ω^{2} x .At t = 2 s, the particle is at x = A sin (ω t) = 1 sin (\frac{π}{4} \cdot 2) = sin (\frac{π}{2}) = 1 m . a = - (\frac{π}{4})^{2} \times 1 = - \frac{π ^{2}}{16} m/s^{2}

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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:

\frac{π ^{2}}{8} m s^{- 2}

- \frac{π ^{2}}{8} m s^{- 2}

\frac{π ^{2}}{16} m s^{- 2}

- \frac{π ^{2}}{16} m s^{- 2}

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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:

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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:

Solution & Step-by-step Explanation

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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: