-If a particle moves such that it retraces its path regularly after regular interval of time,its motion is said to be periodic Ex-Motion of earth around Sun

-If a body in periodic motion moves back and forth over the same path then the motion is said to be oscillatory motion

-Simple harmonic motion is simplest form of oscillatory motion

-SHM is a kind of motion in which the restoring force is propotional to the displacement from the mean position and opposes its increase.Mathematically restoring force is
Where K=Force constant
x=displacement of the system from its mean or equilibrium position
Diffrential Equation of SHM is
d2x/dt2 + ω2x=0
Solutions of this equation can both be sine or cosine functions .We conveniently choose
x=Acos(ωt+φ) where A,ω and φ all are constants

-Quantity A is known as amplitude of SHM which is the magnitude of maximum value of displacement on either sides from the equilibrium position

-Time period (T) of SHM the time during which oscillation repeats itself i.e, repeats its one cycle of motion and it is given by
T=2π/ω where ω is the angular frequency

-Frequency of the SHM is the number of the complete oscillation per unit time i.e, frequency is reciprocal of the time period
Thus angular frequncy

-Velocity of a system executing SHM as a function of time is

-Acceleration of particle executing SHM is

So a=-ω2x

This shows that acceleration is proportional to the displacement but in opposite direction

-At any time t KE of system in SHM is
which is a function varying periodically in time

-PE of system in SHM at any time t is

-Total Energy in SHM
and it remain constant in absense of dissapative forces like frictional forces

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