Question

The figure below correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anticlockwise) are indicated on each figure.

Obtain the corresponding simple harmonic motions of the xprojection of the radius vector of the revolving particle P, in each case.

Answer 1

(a) Let A be any point on the circle shown in fig (a). Draw AM ⊥ to x-axis. Point M refers to x – projection of the radius vector. 

Now, ∠POA = θ = ωt, T = 2s OA = 3cm ⇒ ∠OAM = θ =ωt 

(∵ Alternate angles)

(b) let A be any point on the circles of fig. (b). From A draw AM ⊥ to x-axis

Now ∠MOA= θ = ωt