A particle is executing simple harmonic motio | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) In simple harmonic motion,the velocity $v$ at a displacement $x$ is given by $v = \omega \sqrt{A^2 - x^2}$,where $\omega$ is the angular frequency

Vedclass · Accepted Answer

$\sqrt{4A^2-3x^2}$

Vedclass · Answer

(D) In simple harmonic motion,the velocity $v$ at a displacement $x$ is given by $v = \omega \sqrt{A^2 - x^2}$,where $\omega$ is the angular frequency and $A$ is the amplitude.Initially,the velocity is $v_1 = \omega \sqrt{A^2 - x^2}$.After the blow,the velocity becomes $v_2 = 2v_1 = 2\omega \sqrt{A^2 - x^2}$.Let the new amplitude be $A'$. Since the frequency $\omega$ remains constant,the new velocity at the same position $x$ is $v_2 = \omega \sqrt{A'^2 - x^2}$.Equating the two expressions for $v_2$: $\omega \sqrt{A'^2 - x^2} = 2\omega \sqrt{A^2 - x^2}$.Squaring both sides: $A'^2 - x^2 = 4(A^2 - x^2)$.$A'^2 - x^2 = 4A^2 - 4x^2$.$A'^2 = 4A^2 - 3x^2$.Therefore,the new amplitude is $A' = \sqrt{4A^2 - 3x^2}$.

Similar Questions

Obtain the velocity of a particle executing simple harmonic motion $(SHM)$ by considering the projection of a particle undergoing uniform circular motion.

$A$ simple pendulum performs $S.H.M$ about $x = 0$ with an amplitude $A$ and time-period $T$. The speed of the pendulum at $x = \frac{A}{2}$ will be

$A$ particle executes linear simple harmonic motion with an amplitude of $3\,cm$. When the particle is at $2\,cm$ from the mean position,the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is:

Two particles $P$ and $Q$ start from the origin and execute simple harmonic motion along the $X$-axis with the same amplitude but with periods $3 \ s$ and $6 \ s$, respectively. The ratio of the velocities of $P$ and $Q$ when they meet is

$A$ mass attached to a spring performs $S.H.M.$ whose displacement is $x = 3 \times 10^{-3} \cos(2 \pi t) \text{ m}$. The time taken to obtain maximum speed for the first time is

Vedclass Test Series

Exam Paper Generator

Online Exam Module