The force (F in newton) acting on a particle | vedclass

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

Question

(D) The equation of motion for a particle in simple harmonic motion is $F = -ky$. Given $F + 0.04 \pi^2 y = 0$, we have $F = -0.04 \pi^2 y$. Comparing

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) The equation of motion for a particle in simple harmonic motion is $F = -ky$. Given $F + 0.04 \pi^2 y = 0$, we have $F = -0.04 \pi^2 y$. Comparing this with $F = -ky$, the force constant $k = 0.04 \pi^2 	ext{ N/m}$.The mass of the particle is $m = 90 	ext{ g} = 0.09 	ext{ kg}$.The angular frequency $\omega$ is given by $\omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{0.04 \pi^2}{0.09}} = \sqrt{\frac{4 \pi^2}{9}} = \frac{2 \pi}{3} 	ext{ rad/s}$.The amplitude $A = \frac{6}{\pi} 	ext{ m}$.The maximum velocity $v_{	ext{max}}$ is given by $v_{	ext{max}} = A \omega$.Substituting the values, $v_{	ext{max}} = \left( \frac{6}{\pi} ight) 	imes \left( \frac{2 \pi}{3} ight) = 4 	ext{ m/s}$.

Similar Questions

The velocity of a particle performing simple harmonic motion,when it passes through its mean position is

The equations for the displacements of two particles in simple harmonic motion are $y_1=0.1 \sin \left(100 \pi t+\frac{\pi}{3}\right)$ and $y_2=0.1 \cos \pi t$ respectively. The phase difference between the velocities of the two particles at a time $t=0$ is

Two $S$.$H$.Ms. are represented by equations $y_1 = 0.1 \sin \left(100 \pi t + \frac{\pi}{3} \right)$ and $y_2 = 0.1 \cos (100 \pi t)$. The phase difference between the speeds of the two particles is

$A$ particle performing linear $S.H.M.$ of amplitude $0.1 \,m$ has displacement $0.02 \,m$ and acceleration $0.5 \,m/s^2$. The maximum velocity of the particle in $m/s$ is

An object undergoing simple harmonic motion takes $0.5 \text{ s}$ to travel from one point of zero velocity to the next such point. The angular frequency of the motion is,

Vedclass Test Series

Exam Paper Generator

Online Exam Module