2023 OscillationsSimple Harmonic Motion – Graphs Medium Question 12 of 63 in Oscillations

The x–t graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle…

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 $-\frac{\pi^2}{16}\ ms^{-2}$
B $\frac{\pi^2}{8}\ ms^{-2}$
C $-\frac{\pi^2}{8}\ ms^{-2}$
D $\frac{\pi^2}{16}\ ms^{-2}$

The answer is A.

Solution

From the graph $A=1$, $T=8$, so $\omega=\frac{\pi}{4}$ and $a=-\omega^2x=-\frac{\pi^2}{16}$ at $x=1$.

From the x–t graph, $A=1$, $T=8$ $\Rightarrow\omega=\frac{2\pi}{T}=\frac{\pi}{4}$ At $t=2$, $x=1$: $a=-\omega^2x$ $\Rightarrow a=-\frac{\pi^2}{16}\times1=-\frac{\pi^2}{16}\ m/s^2$

Concept acceleration from x-t graph

Oscillations in past papers

63 questions from this chapter have appeared across 26 exam years.