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  4. A body is performing simple harmonic motion with amplitude a and time period T. Variation of its acceleration (f) with time (t) is shown in figure. If at time t, velocity of the body is v, which of the following graphs is correct?

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Q. A body is performing simple harmonic motion with amplitude $a$ and time period $T$. Variation of its acceleration $(f)$ with time (t) is shown in figure. If at time $t$, velocity of the body is $v$, which of the following graphs is correct?Physics Question Image

Oscillations

Solution:

Acceleration of a particle executing SHM is always directed towards the mean position and its magnitude is directly proportional to that of displacement from mean position. Since acceleration of the particle at initial moment, is maximum possible and is negative, therefore, the particle is at right extreme position at this moment. When the particle is released, it starts to move to the left. It means, velocity starts to increase fromzero initial value to negative value and its magnitude becomes maximum possible at mean position (at $t=T / 4$ ).