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Q. The diagram below shows a sinusoidal curve. The equation of the curve will bePhysics Question Image

Oscillations

Solution:

Let T be the time period; then T2=5π64π64=4π64
T=π8s

Also, A=10 \,cm (from the graph)
The equation of the sinusoidal wave can be written as y=10 \sin (16 t+\phi) cm, where \phi is the initial phase.
From the graph, corresponding to the crest =10 \,cm; when t=3 \pi / 64.
10 \,cm =10 \sin \left[16\left(\frac{3 \pi}{64}\right)+\phi\right] cm
\sin \left[\frac{3 \pi}{4}+\phi\right]=1
or \frac{3 \pi}{4}+\phi=\frac{\pi}{2}
\Rightarrow \phi=-\frac{\pi}{4}
\therefore y=10 \sin \left(16 t-\frac{\pi}{4}\right)