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A particle starts from A/2 and moves tow...

A particle starts from A/2 and moves towards positive extreme as shown below. Find the equation of the SHM. Given amplitude of SHM is A.

Text Solution

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We will solve the above problem with the help of horizontal phasor.
Step 1. Draw a perpendicular line in upward direction from point P on the circle which cuts it at point R & S
Step 2. Horizontal compoment of v(t) at R gives the direction P to A while at S gives P to O. So at t = 0 particle is at R
Step 3. In `Delta ` ORQ
cos `theta = (A//2)/(A) = 60^(@) implies phi = 30^(@)`
So equation of the SHM is x = A sin `(omegat + 30^(@))`

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