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PhysicsSHMMiscellaneousMedium2 minPYQ_2014

PhysicsMediumsingle choice

The displacement of a particle in a periodic motion is given by $y = 4 cos^{2} (\frac{t}{2}) sin (1000 t)$ . This displacement may be considered as the result of superposition of $n$ independent harmonic oscillations. Here $n$ is

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Given, $Y = 4 cos^{2} (\frac{t}{2}) \cdot sin (1000 t)$ $= 2 \times 2 cos^{2} (\frac{t}{2}) \cdot sin (1000 t)$ $[∵ 2 cos^{2} \frac{t}{2} = (1 + cos t)]$ $= 2 (1 + cos t) sin (1000 t)$ $= 2 sin (1000 t) + 2 cos t \cdot sin (1000 t)$ $= 2 sin (1000 t) + 2 sin (1000 t) \cdot cos t$ $= 2 sin (1000 t) + sin (1000 t + t)$ $[∵ - 2 sin A \cdot cos B = sin (A + B) + sin (A - B)] = 2 sin (1000 t) + sin (1001 t) + sin (999 t)$ So, $n = 3$

Stream:WBJEESubject:PhysicsTopic:SHMSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2014

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