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

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Solution :`y = 4 cos^(2) (t/2) sin (1000t)`
`y=2(1+cost) sin(1000t)(THEREFORE 2cos^(2) THETA -1 + cos 2theta)`
`=2sin(1000t) +sin(1001t) + sin(999t)`
`(therefore 2sinA COSB = sin(A+B) +sin(A-B))`


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