The position x of particle moving along x-axis varies with time t as x=A sin (ω t) where A and ω are positive constants. The acceleration a of particle varies with its position (x) as

Question

The position x of particle moving along x-axis varies with time t as x=A sin (ω t) where A and ω are positive constants. The acceleration a of particle varies with its position (x) as (A) a=A x (B) a=-ω2 x (C) a=A ω x (D) a=ω2 × A

Tardigrade Admin · Accepted Answer

x=A sin ω t (d x/d t)=A ω cos ω t ⇒ (d2 x/d t2)=-A ω2 sin ω t ⇒ a=-ω2 x (∵ A sin ω t=x)

Q. The position $x$ of particle moving along $x$ -axis varies with time $t$ as $x = A sin (ω t)$ where $A$ and $ω$ are positive constants. The acceleration a of particle varies with its position $(x)$ as

$a = A x$

$a = - ω^{2} x$

$a = A ω x$

$a = ω^{2} \times A$

$x = A sin ω t$
$\frac{d x}{d t} = A ω cos ω t$
$\Rightarrow \frac{d ^{2} x}{d t ^{2}} = - A ω^{2} sin ω t$
$\Rightarrow a = - ω^{2} x (∵ A sin ω t = x)$

Q. 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

a=Ax

a=−ω2x

a=Aωx

a=ω2×A