Question

The displacment of a particle as a function of time t is given by y=4*cos^2(t/2)sin(1000t).

Answer 1

Answer:

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y = 4 cos2 (1/2 t) sin (1000 t)

  =  2 x 2 cos2(t/2)sin (1000 t)

  = 2 x (1 + cos t) sin (1000 t)

  = 2 sin (1000 t) + 2 cos t sin (1000 t)

  = 2 sin (1000 t) + sin [(1000+1)t] +sin [(1000−1)t]

  =  2 sin (1000 t) + sin (1001)t +sin (999)t

  = y1 + y2 + y3

As the above expression involves three different waves the displacement given is a result of superposition of three different waves