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.

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

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

A geologist finds the frequency of a pendulum is 0.3204 Hz when it is located at a point where acceleration due to gravity is 9.8000 m/s2. What is the value of ‘g’ at a location where the pendulum’s frequency is 0.3196 Hz? Since f = 0.3204 Hz when g = 9.8000 m/s2, we can calculate the length of the pendulum. T = 3.1211 sec Use this length to calculate gravity when f = 0.3196 Hz. T = 3.1289 sec g = 9.7510 m/s2 = 2.4181 m