When a body or a moving particle repeats its motion along a definite path after regular interval
of time, its motion is said to be Periodic Motion and interval of time is called time period
or harmonic motion period (T). The path of periodic motion may be linear, circular, elliptical or
any other curve. For example, rotation of earth about the sun.
EQUATION OF SIMPLE HARMONIC MOTION (SHM) :
The necessary and sufficient condition for SHM is
Note : In the figure shown, path of the particle is on a straight line.
Consider a particle moving on a circle of radius A with a
constant angular speed ? as shown in figure
GRAPHICAL REPRESENTATION OF DISPLACEMENT, VELOCITY
& ACCELERATION IN SHM
ENERGY OF SHM
1 Kinetic Energy (KE)
SPRING-MASS SYSTEM
In series combination, tension is same in all the springs & extension will be different. (If k is same
then deformation is also same )
In series combination , extension of springs will be reciprocal of its spring constant.
METHOD’S TO DETERMINE TIME PERIOD
If a heavy point mass is suspended by a weightless, inextensible and perfectly
flexible string from a rigid support, then this arrangement is called a simple
pendulum
Time Period of Simple Pendulum in accelerating Reference Frame
COMPOUND PENDULUM / PHYSICAL PENDULUM
In torsional pendulum, an extended object is suspended at the centre by a light torsion
wire. A torsion wire is essentially inextensible, but is free to twist about its axis. When
the lower end of the wire is rotated by a slight amount, the wire applies a restoring torque
causing the body to oscillate (rotate) about vertical wire, when released
SUPERPOSITION OF TWO SHM’S
