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The coordinates of a particle moving in ...

The coordinates of a particle moving in a plane are given by x (t) = a cos (pt) and y (t) = b sin (pt), where a, b (`lt` a), and p are positive constants of appropriate dimensions. Then:

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The given wave can be written as the sum of two component waves `y_(1)=0.2 sin (0.5x-30t) and y_(2)=0.2 sin (0.5x+30t)`
Now` omega=30(rad)/(s) and k=0.5 cm^(-1)`
`:.` Freqency of `f=(omega)/(2pi)=(15)/(pi)Hz`
amplitude `A=0.2 cm`
and were speed, `V=(omega)/(K)=(30)/(0.5)=60 cm//s`
(b) particle velocity
`v_(p)(x,t)=(dy)/(dt)=-12 sin (0.5x)sin(30t)`
`v_(p)(x=2.4 cmt,=0.8s)`
`=-12 sin(1.2 sin(24)=10.12 cm//s`
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