A particle of mass m is under the influence o | vedclass

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

Question

(C) Given that,the force acting on the particle is $F = -kx + F_0$. We can rewrite this as $F = -k(x - \frac{F_0}{k})$. Let $y = x - \frac{F_0}{k}$,th

Vedclass · Accepted Answer

about $x = \frac{F_0}{k}$ with $\omega = \sqrt{\frac{k}{m}}$

Vedclass · Answer

(C) Given that,the force acting on the particle is $F = -kx + F_0$. We can rewrite this as $F = -k(x - \frac{F_0}{k})$. Let $y = x - \frac{F_0}{k}$,then the force becomes $F = -ky$. This is the standard form of the restoring force for Simple Harmonic Motion $(SHM)$,where the mean position is defined by $F = 0$. Setting $F = 0$,we get $-k(x - \frac{F_0}{k}) = 0$,which implies $x = \frac{F_0}{k}$. Thus,the particle oscillates about the mean position $x = \frac{F_0}{k}$. Comparing $F = -ky$ with the standard $SHM$ equation $F = -m\omega^2 y$,we get $m\omega^2 = k$. Therefore,the angular frequency is $\omega = \sqrt{\frac{k}{m}}$.

$A$ particle of mass $m$ is under the influence of a force $F = (-kx + F_0) \text{ N}$. The particle,when disturbed,will oscillate

Similar Questions

The motion of a particle as per $x = A \sin \omega t + B \cos \omega t$ is :-

On an average,a human heart is found to beat $75$ times in a minute. Calculate its frequency and period.

Define displacement variable and periodic function.

The equation of motion of a particle is given by $x = a \sin(50t + \frac{\pi}{3}) \text{ cm}$. The particle will come to rest at time $t_1$ and it will have zero acceleration at time $t_2$. The $t_1$ and $t_2$ respectively are . . . . . . .

Why is the periodic time $T = \frac{2\pi}{\omega}$ taken for the function $f(t) = A \cos \omega t$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module