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Obtain the equation for SHM of the Y-pro...

Obtain the equation for SHM of the Y-projection of the radius vector of the revolving particle P in case (a) and (b) of figure.

Text Solution

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(a) Here, `T= 3s, A = 2 cm, phi = (60)^(@)= (pi)/(3) rad`
`omega = (2pi)/(T) = (2pi)/(3) rad s^(-1)`.
Equation for SHM of Y-Projection of radius vector of the revolving particle P.
`y= A sin (omega t+ phi)`
`y = 2sin ((2pi)/(3)t+(pi)/(3))cm`.
(b) Here, `T= 3 min= 60s, A = 3 cm, phi = +(90)^(@)= +(pi)/(2) rad s`
`omega = (2pi)/(T) = (2pi)/(60)`
`=(pi)/(30) rad s^(-1)`.
Equation for SHM of Y-Projection of radius vector of the revolving particle P.
`y= A sin (omega t+ phi)`
`y = 3sin ((pi)/(30)t+(pi)/(2))`
`= 3 sin ((pi)/(2)+(pi)/(30)t)`
`y= 3cos ((pi)/(30)t)cm " "[therefore sin ((pi)/(2)+theta)= cos theta]`.
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