Test Index

Simple Harmonic Motion

Section: Physics

Question : 22 of 23

Marks: +1, -0

Solution:

The equation of single harmonic motion is x = A sin

\left(\frac{2\pi}{T} t\right)

, where A is amplitude and T is the time period of the motion.

From the given figure, A = 1 and T = 8. Thus,

x = sin

\left(\frac{\pi}{4} t\right)

x = sin

\left(\frac{\pi}{t}\right)

The acceleration is

a =

\frac{d^2x}{dt^2}

-\frac{\pi^2}{1} \sin\left(\frac{\pi}{4} t\right)

At time t =

\frac{4}{3}

s , the acceleration is

a =

-\frac{\pi^2}{16} \sin\left(\frac{\pi}{4} \times \frac{4}{3}\right)

= -

\frac{\sqrt{3}}{32} \pi^2 \text{cm/s}^2

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