# Simple Harmonic Motion

• An object in simple harmonic motion (SHM) repeats its motion over regular intervals of time, also known as its period.
• SHM follows a sinusoidal pattern, it can be described using sine or cosine functions.
• In SHM, the restoring force is directly proportional to the displacement of the object from its equilibrium position and acts in the direction opposite to the displacement.
• The angular frequency (ω) of the motion is the rate of change of the angle that the motion makes during its oscillation, measured in radians per second.
• The amplitude of SHM refers to the maximum displacement of the object from its equilibrium position.
• The phase constant or phase angle (φ) in SHM defines the starting point on the sinusoidal wave.

# Springs

• A spring obeys Hooke’s Law which states that the force required to extend or compress a spring by a certain distance is proportional to that distance.
• The constant of proportionality is known as the spring constant k, measured in N/m.
• The potential energy stored in a spring when it is either compressed or extended is given by the equation PE = 1/2 kx².
• Simple harmonic motion of a spring can be described by the equation x = A cos(ωt + φ), where x is displacement, A is the amplitude of the motion, ω is the angular frequency, and φ is the phase constant.

# Pendulums

• A simple pendulum consists of a mass (the pendulum bob) attached to a string or rod of negligible mass which swings back and forth under the influence of gravity.
• The time for one complete oscillation or swing back and forth, known as the period of a pendulum, depends on the length of the pendulum and the acceleration due to gravity.
• The period of a simple pendulum can be given by the equation 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 small displacements, a pendulum exhibits SHM.
• In real-world pendulums, damping and friction will cause the oscillations to gradually decrease in amplitude. However, in an ideal simple pendulum, the oscillations continue indefinitely.