Damped & Forced Oscillations

# Damped & Forced Oscillations | Physics Class 11 - NEET PDF Download

Damped Oscillations

Oscillations with a decreasing amplitude with time are called damped oscillations.

The displacement of the damped oscillator at an instant t is given by

x = xoe– bt / 2m cos (ω’ t + φ)

where xoe– bt / 2m is the amplitude of oscillator which decreases continuously with time t and ω’.

The mechanical energy E of the damped oscillator at an instant t is given by

E = 1 / 2 kx2oe– bt / 2m

Un-damped Oscillations

Oscillations with a constant amplitude with time are called un-damped oscillations.

Forced Oscillations

Oscillations of any object with a frequency different from its natural frequency under a periodic external force are called forced oscillations.

Resonant Oscillations

When an external force is applied on a body whose frequency is an integer multiple of the natural frequency of the body, then its amplitude of oscillation increases and these oscillations are called resonant oscillations.

Lissajous’ Figures

If two SHMs are acting in mutually perpendicular directions, then due to then: superpositions the resultant motion, in general, is a curve loop. The shape of the curve depends on the frequency ratio of two SHMs and initial phase difference between them. Such figures are called Lissajous’ figures.

1. Let two SHMs be of same frequency (e.g., x = a1 sinωt and y = a2 sin (omega;t + φ), then the general equation of resultant motion is found to be

x2 / a21 + y2 / b22 – 2xy / a1a2/sub> cos φ = sin2 φ

The equation represents an ellipse. However, if φ = O° or π or nπ, then the resultant curve is a straight inclined line.

2. Let two SHMs be having frequencies in the ratio 1 : 2, then, in general, the Lissajous figure is a figure of eight (8).

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## Physics Class 11

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## FAQs on Damped & Forced Oscillations - Physics Class 11 - NEET

 1. What is a damped oscillation?
Ans. A damped oscillation refers to a type of oscillatory motion where the amplitude of the oscillation gradually decreases over time due to the presence of an external damping force or resistance.
 2. How does damping affect an oscillation?
Ans. Damping affects an oscillation by reducing its amplitude and slowing down its motion. As the damping force increases, the energy of the oscillating system is dissipated, causing the oscillation to gradually come to a stop.
 3. What are forced oscillations?
Ans. Forced oscillations occur when an external force is applied to an oscillating system, causing it to oscillate with a frequency different from its natural frequency. The external force can either be periodic or non-periodic.
 4. How does the frequency of the applied force affect forced oscillations?
Ans. The frequency of the applied force plays a crucial role in forced oscillations. When the frequency of the applied force matches the natural frequency of the system, resonance occurs, leading to a significant increase in the amplitude of the oscillation. If the frequencies do not match, the amplitude remains relatively small.
 5. Can a damped oscillation be forced?
Ans. Yes, a damped oscillation can be forced by applying an external force to the system. In this case, the damping force and the applied force act simultaneously, resulting in a combination of damping and forced oscillations. The behavior of the system will depend on the relative strengths of the damping force and the applied force.

## Physics Class 11

102 videos|411 docs|121 tests

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