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 (he was saying something about Legendre's Polynomials). 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.

Post edited by: Neel, at: 2008/05/15 04:27

i didn't get your question very clearly....
if u hv to find the distance traveled..can't it simply be done like this....
lets say the time period is T (T=2pi/w)....and u have to find the distance traveled upto time t (where t = nT + q) ---basically, what i'm saying is find out how many time periods are included in time t....say n...then distance corresponding to that will be n*(4A) because in one time period, distance covered is 4A...
for the remaining time q, do integral(mod(Asin(wt))) in the interval (0,q)
Is anything wrong here?

To Admin: please integrate math symbols in the forums....it would be much easier to type then...

you're wrong. the answer is beyond yours and my comprehension

wud u pls tell me whats wrong with this????

btw, we shuldnt think like something is beyond our comprehension etc

I'll post the exact question:

A particle moves along the x axis according to the law x = a sin wt. Find the distance that the particle covers during the time interval t (starting from 0)

The answer is:

n is a whole number of the ratio 2wt/π

if n is even,
s = a {n + sin (wt - nπ/2)}

if n is odd,
s = a {n + 1 - cos (wt - nπ/2)}

On reading it a bit more carefully, I think Prems method is the correct way to do this.. Put in more paragraphs!

Thanks man.

Post edited by: Neel, at: 2008/05/25 04:29