The position of x of particle moving along x axis varies with time t as x=asin(wt)
Answers
answer : option (a) a = -ω²x
complete question is -> The position x of particle moving along x-axis varies with time t as x= Asin(ωt) where A and ω are positive constants. The acceleration a of particle varies with its position (x) as,
(1) a= Ax , (2) a= -ω²x, (3) a= Aωx , (4) a= ω²xA
position of particle varies as, x = Asin(ωt)......(1)
differentiating with respect to time,
dx/dt = Aωcos(ωt)
again differentiating with respect to time,
d²x/dt² = -Aω²sin(ωt)
from equation (1) we get, d²x/dt² = -ω²x
as we know, acceleration, a = d²x/dt²
so, a = -ω²x
hence, acceleration of particle varies its position as a = -ω²x
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