Oscillations

PART 2

(1) Some system Executing SHM

a)Oscillations of a Spring mass system

-In this case particle of mass m oscillates under the influence of hooke's law restoring force given by F=-Kx where K is the spring constant

Angular Frequency ω=√(K/m)

Time period T=2π√(m/K)

And frequency is =(1/2π)√(K/m)

Time period of both horizontal ans vertical oscillation are same but spring constant have diffrent value for horizontal and vertical motion

b) Simple pendulum

-Motion of simple pendulum oscillating through small angles is a case of SHM with angular frequency given by
ω=√(g/L)
and Timeperiod
T=2π√(L/g)
Where L is the length of the string.

-Here we notice that period of oscillation is independent of the mass m of the pendulum

c) Compound Pendulum

- Compound pendulum is a rigid body of any shape,capable of oscillating about the horizontal axis passing through it.
-Such a pendulum swinging with small angle executes SHM with the timeperiod

T=2π√(I/mgL)

Where I =Moment of inertia of pendulum about the axis of suspension
L is the lenght of the pendulum

(2) Damped Oscillation

-SHM which continues indefinitely without the loss of the amplitude are called free oscillation or undamped and it is not a real case

- In real physical systems energy of the oscillator gradually decreases with time and oscillator will eventually come to rest.This happens because in acutal physical systems,friction(or damping ) is always present

-The reduction in amplitude or energy of the oscilaltor is called damping and oscillation are call damped

(3) Forced Oscillations and Resonance.

- Oscillations of a system under the influence of an external periodic force are called forced oscillations

- If frequency of externally applied driving force is equal to the natural frequency of the oscillator resonance is said to occur