1. Simple Harmonic Motion:
repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side. The time interval of each complete vibration is the same (the period - T), and the force responsible for the motion is always directed toward the equilibrium position and is directly proportional to the distance from it.

2. Two common examples in mechanics:
The pendulum
Oscillating mass on a spring

3. Oscillating mass on a spring
Since the forces and displacement vary at every point, SHM is best described in terms of its PERIOD.
The pendulum
Oscillating mass on a spring
Where :
m = mass on the
spring (kilograms)
T = period (seconds)
= length of the
pendulum (meters)
k = spring constant (N/m)
g = 9.8 m/s2

4. A geologist finds the frequency of a pendulum is
Hz when it is located at a point where
acceleration due to gravity is m/s2. What is the
value of ‘g’ at a location where the pendulum’s
frequency is Hz?
Since f = Hz when g = m/s2, we can calculate the length of the pendulum.
T = sec
Use this length to calculate gravity when f = Hz.
T = sec
g = m/s2
= m