This document discusses simple harmonic motion and provides useful formulas. It explains that the period of a simple pendulum is calculated as T = 2π√l/g, where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity. For an elastic spring undergoing simple harmonic motion, the total energy is calculated as the kinetic energy (1/2mv^2) plus the potential energy (1/2kx^2), where k is the spring constant. The document also states that the total energy is equal to the maximum potential energy when the kinetic energy is zero, and equal to the maximum kinetic energy when the potential energy is zero.

1. PHYSICS
SIMPLE HARMONIC MOTION
Short revision series

2.  s
θ
PP’
K.E = 0
V = 0
P.E = max
= mgh
P.E = 0
V = max
K.E = max
=1/2 mv2
h

3. Useful formulae
 Period of a simple pendulum
T = 2π √l/g
l = lenght of simple pendulum
g = acceleration due to gravity
T = period
 Angular velocity ω = θ/t
 Θ = angle turned by body
t = time takken
Linear velocity v = rω

4.  Acceleration of SHM
 Angular acceleration is the rate of change of
angular velocity with time
 α = a/r
 a = αr
 Frequency – number of complete revolutions
per min
 f = 1/T

5. Energy of SHM
 shm
θ
PP’
K.E = 0
V = 0
P.E = max
= mgh
P.E = 0
V = max
K.E = max
=1/2 mv2
h

6.  In an elastic spring, F =kx; F being the force
used to stretch the spring by a distance, and
k = force constant
 Work done = ½ force x displacement x
 Kx/2 x X = ½ kx
 Therefore energy in the spring = ½ kx2
 The maximum P.E = ½ kx2

7.  K.E at any instant = ½ mv2
 At position of maximum displacement v = 0
therefore K.E = 0
 At that point the total energy = K.E + P.E = 0
+ ½ kx2
Total energy = ½ kx2

8.  At equilibrum when K.E is max, P.E = 0
 Total energy will be = K.E + P.E = ½ mv2 + 0
= ½ mv2
 But at any other positions besides position of
maximum displacement and position of
equilibrum
total energy = KE + PE = ½ mv2 + ½ kx2

9.  At position P and P’ which is when there is
maximum displacement TE = PE + 0 = mgh
θ
PP’
K.E = 0
V = 0
P.E = max
= mgh
P.E = 0
V = max
K.E = max
=1/2 mv2
h

10. End