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) The condition for the mean position in simple harmonic motion is that the net restoring force must be zero.Given the force equation: $F = -kx + F_

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) The condition for the mean position in simple harmonic motion is that the net restoring force must be zero.Given the force equation: $F = -kx + F_0$.At the mean position,$F = 0$,so $0 = -kx + F_0$,which gives $x = F_0/k$.To find the angular frequency $\omega$,we rewrite the force equation in terms of the displacement from the mean position $x' = x - F_0/k$. Then $x = x' + F_0/k$.Substituting this into the force equation: $F = -k(x' + F_0/k) + F_0 = -kx' - F_0 + F_0 = -kx'$.Comparing this with the standard $SHM$ equation $F = -m\omega^2 x'$,we get $m\omega^2 = k$,which implies $\omega = \sqrt{k/m}$.Therefore,the particle oscillates about $x = F_0/k$ with an angular frequency $\omega = \sqrt{k/m}$.

$A$ particle of mass $m$ is under the influence of a force $F$ which varies with the displacement $x$ according to the relation $F = -kx + F_0$,where $k$ and $F_0$ are constants. The particle,when disturbed,will oscillate:

Similar Questions

Write the phase difference between displacement and velocity,displacement and acceleration,and velocity and acceleration for a particle executing Simple Harmonic Motion $(SHM)$.

What are called normal modes of oscillation of a system?

What is the value of frequency in the differential equation of $SHM$ $\frac{d^{2}x}{dt^{2}} + 100x = 0$?

Equations $y = 2A \cos^2 \omega t$ and $y = A (\sin \omega t + \sqrt{3} \cos \omega t)$ represent the motion of two particles.

$A$ particle of mass $0.4 \text{ kg}$ executes simple harmonic motion of amplitude $0.4 \text{ m}$. When it passes through the mean position,its kinetic energy is $256 \times 10^{-3} \text{ J}$. If the initial phase of the oscillation is $\pi / 4$,then the equation of its motion is

Vedclass Test Series

Exam Paper Generator

Online Exam Module