Write the equation of angular frequency and amplitude for damped oscillation.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) For a damped harmonic oscillator,the equation of motion is given by $m \frac{d^2x}{dt^2} + b \frac{dx}{dt} + kx = 0$.
The amplitude of a damped oscillation decreases exponentially with time and is given by $A(t) = A_0 e^{-bt/2m}$,where $A_0$ is the initial amplitude,$b$ is the damping constant,$m$ is the mass,and $t$ is time.
The angular frequency of the damped oscillation is given by $\omega' = \sqrt{\frac{k}{m} - \left(\frac{b}{2m}\right)^2}$,where $k$ is the spring constant.

Explore More

Similar Questions

$A$ block of mass $100 \,g$ is connected to an elastic spring of spring constant $450 \,N m^{-1}$ and oscillates vertically. The block-spring system is in a viscous surrounding medium with a damping constant $b = 69.3 \,g \,s^{-1}$. Calculate the time in which the amplitude of oscillations drops to half of its initial value. (Take $\ln 2 = 0.693$) (in $\,s$)

Sometimes when the speed of a vehicle is increased,its body starts to bounce. Why?

The displacement of a damped harmonic oscillator is given by $x(t) = e^{-0.1t} \cos(10\pi t + \varphi)$. The time taken for its amplitude of vibration to drop to half of its initial value is close to .... $s$

In the case of a forced vibration,the resonance curve becomes very sharp when the

What is pure simple harmonic oscillation? Why is it not $100 \%$ possible in practice?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo