x= Asin(wt)------------------------the particle moves with this trajectory. the wave travels in the y direction.



the question asks us to derive an expression for the distance moved by the particle in time "t" starting fom t=0.



i came up with a solution. but i'm getting stuck at one point. My prof. tells me that higher calculus is rquired for this question which is beyond the scope of the JEE. i think i have an alternate approach. PLease help.





Consider a particle undergoing UCM. describing a circle of radius "A" with angular freq. "w", at any arbitrary position , say (Acosθ , Asinθ), now the projection of the radial vector to this point on the x axis represents the distance of the particle undergoing SHM according to the given eqn. from the origin, i.e. the mean position.



thus, x= Acosθ----------- (1)



=>θ =nπ/2 - wt ---------------(here "n" is an odd integer)



now the arc length the UCM particle covers (lets call it "P" for convinience) corresponds to the linear displacement of the SHM particle (lets call it Q).....now this will be valid only when both these quantities are infinitismly small so we have to use derivatives.





consider an arc length covered by P on sweeping an angle of Δθ, say



L = AΔθ



=> dL/dt = A dθ/dt



= A w



the problem is i am not able to relate the motion of P with that of Q, mathematically. the theory part is pretty clear i suppose.