# Forced, Damped oscillations and Resonance

• The oscillations of a body whose amplitude goes on decreasing with time are defined as damped oscillations where F = −bV where 'b' is damping constant.
• In forced oscillations the amplitude of oscillations decreases exponentially due to damping force like frictional force , viscous force  and  hysteresis etc.

Amplitude A = xm e−γt γ = b/2m

• The oscillations in which a body oscillates under the influence of an external force are known as forced oscillations.

F = −bv −Kx + Fm cos w mt

• When the frequency of the external periodic forces is equal to the natural frequency of oscillator the amplitude increases to maximum value the phenomenon is called resonance

\tt T = 2 \pi \sqrt{\frac{M}{K}}

### View the Topic in this video From 0:26 To 12:05

Disclaimer: Compete.etutor.co may from time to time provide links to third party Internet sites under their respective fair use policy and it may from time to time provide materials from such third parties on this website. These third party sites and any third party materials are provided for viewers convenience and for non-commercial educational purpose only. Compete does not operate or control in any respect any information, products or services available on these third party sites. Compete.etutor.co makes no representations whatsoever concerning the content of these sites and the fact that compete.etutor.co has provided a link to such sites is NOT an endorsement, authorization, sponsorship, or affiliation by compete.etutor.co with respect to such sites, its services, the products displayed, its owners, or its providers.

1. The displacement of the oscillator is given by
x(t) = Aebt/2m cos (ω't + Φ)
where, ω' the angular frequency of the damped oscillator is given by
\omega' = \sqrt{\frac{k}{m} - \frac{b^{2}}{4m^{2}}}

2. The mechanical energy E of the damped oscillator is given by
E(t) = \frac{1}{2}kA^{2} e^{-bt/m}