SATHEE: Simple Harmonic Motion 2 Question 2

Simple Harmonic Motion 2 Question 2

2. The $x$ - $t$ graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t = 4 / 3 s$ is

(a) $\frac{\sqrt{3}}{32} π^{2} c m s^{- 2}$

(b) $\frac{- π^{2}}{32} c m s^{- 2}$

(d) $- \frac{\sqrt{3}}{32} π^{2} c m s^{- 2}$

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Answer:

Correct Answer: 2. (d)

Solution:

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

$\begin{aligned} \Rightarrow x = A \sin ω t \\ ∴ a = - ω^{2} x = - \frac{π^{2}}{16} \sin \frac{π}{4} t \end{aligned}$

Substituting $t = \frac{4}{3} s$ , we get

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Simple Harmonic Motion 2 Question 2

2. The x - t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t=4/3s is

Answer:

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2. The $x$ - $t$ graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t = 4 / 3 s$ is