the position X of particle moving along x-Asin(wt) where A and every are positive constant. the acceleration a of particle varies with its position X as
Answer (1)
1st Feb, 2020
Hello,
The position of particle in X direction varies as :
x = A sin(wt )............ ( 1 )
Differentiate the above equation with respect to time to find the velocity of particle at any instant:
So, dx / dt = v = w.A.cos(wt)......... ( 2 )
Now, we know that acceleration is the rate of change of velocity with respect to time.
So, now differentiating equation 2 with respect to time to find velocity.
a = dv / dt = -w^2. A. ( sin wt )
From eqn 1,
a = - w^2 . x
So, the acceleration of particle varies as, a = - w^2 . x
Best Wishes.
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