simple harmonic motion

• Periodic motion is the motion of an object that regularly repeats – the object returns to a given position after a fixed time interval.
• A very common type of periodic motion is simple harmonic motion (SHM). It is a type of periodic motion where the resting force is proportional to the displacement of the body from its equilibrium position.
• Fs = -kx where; Fs = restoring force or spring force x = displacement from the equilibrium position (negative, opposite direction with Fs) k = proportionality constant
• This restoring force acts in a direction opposite that of the displacement. Proportionality: a ∝ -x
• 1. There is repetitive movement back and forth through an equilibrium, or central, position, so the maximum horizontal or vertical displacement on one side of this position is equal to the maximum horizontal displacement on the other
• so that, the relationship of a pendulum’s acceleration and displacement is “The acceleration of the pendulum is inversely proportional to the direction of the displacement”
• 2. The time interval of each complete vibration is the same (periodic)
• 3. The force responsible for the motion (restoring force) is always directed horizontally or vertically towards the equilibrium position and is directly proportional to the distance from it
• A body of mass (m) oscillating on one end of an elastic spring also known as the mass-spring system