A body is performing simple harmonic motion of amplitude A and time period T . The figure shows position-time graph of the body. At any time t , acceleration of the body is f , then which of the following graphs is/are appropriate?

Question

A body is performing simple harmonic motion of amplitude A and time period T . The figure shows position-time graph of the body. At any time t , acceleration of the body is f , then which of the following graphs is/are appropriate? Question

(A)

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

Since initial phase is (π /2) as per the given graph. Using the equation of position of SHM x = A sin (. ω t + (π /2) .) ⇒ x = A cos ω t ⇒ acceleration f = (d2 x/d t2) = - A ω 2 cos ω t Which is represented in option third.

Q. A body is performing simple harmonic motion of amplitude $A$ and time period $T$ . The figure shows position-time graph of the body. At any time $t$ , acceleration of the body is $f$ , then which of the following graphs is/are appropriate?

Since initial phase is $\frac{π}{2}$ as per the given graph.
Using the equation of position of SHM $x = A s in (ω t + \frac{π}{2})$
$\Rightarrow x = A cos ω t$
$\Rightarrow$ acceleration $f = \frac{d ^{2} x}{d t ^{2}} = - A ω^{2} cos ω t$
Which is represented in option third.

Q. A body is performing simple harmonic motion of amplitude A and time period T . The figure shows position-time graph of the body. At any time t , acceleration of the body is f , then which of the following graphs is/are appropriate?

Since initial phase is 2π​ as per the given graph. Using the equation of position of SHM x=Asin(ωt+2π​) ⇒x=Acosωt ⇒ acceleration f=dt2d2x​=−Aω2cosωt Which is represented in option third.

Q. A body is performing simple harmonic motion of amplitude $A$ and time period $T$ . The figure shows position-time graph of the body. At any time $t$ , acceleration of the body is $f$ , then which of the following graphs is/are appropriate?

Since initial phase is $\frac{π}{2}$ as per the given graph.
Using the equation of position of SHM $x = A s in (ω t + \frac{π}{2})$
$\Rightarrow x = A cos ω t$
$\Rightarrow$ acceleration $f = \frac{d ^{2} x}{d t ^{2}} = - A ω^{2} cos ω t$
Which is represented in option third.