“Damped Oscillations” MHT-CET Class 12 Physics Crash Course | Chapter Oscillations
In this session G.S. Khairnar discussed the theory and MCQ’s of “Damped Oscillations”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.
Damped Oscillations:-
Hello dear students we know that there are two types of oscillations, viz: free oscillations and forced oscillations.When the object is oscillating due to its natural frequency, is said to have free oscillations. Whereas when oscillations of particles are due to external periodic forces, then the oscillations as known as forced oscillations. Let’s learn some important characteristics of free and forced vibrations.
Free Vibrations:-
The body is set up into vibrate with its own natural frequency called as free vibrations.
e.g. oscillations of simple pendulum, vibrations of tuning fork.
Characteristics:-
- Frequency depends upon nature of body.
- Energy of oscillating body goes decreasing.
- The amplitude of oscillations goes on decreasing due to presence of air and frictional forces.
- The force does not continuously acts on body.
Forced vibrations:-
The body is set in to vibrations due to external periodic forces called as forced vibrations.
Characteristics:-
- Frequency depends upon external frequency.
- Energy of oscillating body remains constant.
- The amplitude of oscillations remains constant.
- The force continuously acts on body.
If any particle is performing oscillations with constant amplitude throughout, then the oscillations are known as undamped oscillations. When the motion of an oscillator is reduced by an external force, the oscillator and its motion are said to be damped.
Let’s define and learn the concept of damped oscillations in detail……..!
Definition:
Periodic oscillations of gradually decreasing amplitude are called damped harmonic oscillations and the oscillator is called damped harmonic oscillator.
An idealized example of damped oscillator is shown in figure below.
Block of mass ‘m’ oscillates vertically on a spring with spring constant k. From the block, a rod extends to Vane that is submerged in liquid experiences damping force. The damping force depends upon nature of surrounding medium.
The damping force Fd is directly proportional to velocity ‘v’ of vane and block.
Fd α v i.e. Fd =-b v
Where ‘b’ is damping constant and negative sign indicates thatFd opposes the motion.
The force on the block from spring is, Fs =-k x. Let us assume that the gravitational force on the block is negligible compared to Fd& Fs. Thus the total force acting on the block at any time ‘t’ is,
The above is the differential equation for damped harmonic oscillations.
Damped Oscillations
Let’s solve following MCQ’s….!
Q.1) Periodic oscillations of gradually decreasing amplitude are known as…
a) free oscillations
b) forced oscillations
c) damped oscillations
d) none of these
Answer
c) damped oscillations
Q.2) Which among the following represents the correct differential equation for damped harmonic oscillations…
Q.3) Particle is performing oscillations with constant amplitude throughout, then the oscillations are…..
a) free oscillations
b) forced oscillations
c) damped oscillations
d) undamped oscillations
Answer
d) undamped oscillations
Q.4) Damping force acting on the vane of damped harmonic oscillator is directly proportional to…..
a) displacement
b) velocity
c) acceleration
d) buoyant force
Answer
b) velocity
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