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Oscillations
Simple Harmonic Motion – Graphs
1 question from 1 paper, each with its answer.
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Concepts tested
- acceleration from x-t graph
All Questions
2023 1 question
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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:
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 $t=2$, $x=1$: $a=-\omega^2x$ $\Rightarrow a=-\frac{\pi^2}{16}\times1=-\frac{\pi^2}{16}\ m/s^2$