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Plot the corresponding reference circle ...

Plot the corresponding reference circle for given SHM, indicate the initial `( t=0)` position of the paritcle, the radius of the circle , and the angular speed of the rotating paritcle. Consider anticlockwise direction for rotation. `x= - 3 sin ( 2 t + (pi)/(4))` (Express in the form , `x=` Acos ( omega t + phi))`.

Text Solution

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`x= - 3 sin ( 2t + (pi)/(4))`
`= 3 xos ((pi)/(2)+(2 t +(pi)/(4)))` as `cos ( 90^(@) + theta) = - sin theta`
`= 3 cos ( 2t+ ( 3pi)/(4))`
Comparing with `x= A cos ( omega t + phi)` ,we get
`A =3, omega =2 , phi = (pi)/(2)+(pi)/(4)= (3pi)/(4)`
The reference circle is as shown in figure.
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