When a mass m is hung on a spring, the spring stretches 6.0 cm. Determine its period of vibration if it is then pulled down a little and released.

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Simple harmonic motion (SHM) is a type of periodic motion where an object oscillates about a fixed point, called the equilibrium position, with a constant amplitude (maximum displacement) and a constant frequency (number of oscillations per unit time).

Characteristics of SHM:

1. _Periodic motion_: The object moves back and forth in a regular, repeating pattern.
2. _Fixed equilibrium point_: The object oscillates about a fixed point, returning to it after each cycle.
3. _Constant amplitude_: The maximum displacement from the equilibrium point remains constant.
4. _Constant frequency_: The number of oscillations per unit time remains constant.
5. _Sinusoidal motion_: The displacement, velocity, and acceleration of the object vary sinusoidally with time.

Examples of SHM:

1. Massspring system
2. Pendulum (for small angles)
3. Vibrating strings
4. Oscillating circuits (LC circuits)

Equations of SHM:

1. Displacement: x(t) = A cos(ωt + φ)
2. Velocity: v(t) = Aω sin(ωt + φ)
3. Acceleration: a(t) = Aω² cos(ωt + φ)

where:
A = amplitude
ω = angular frequency
φ = phase angle
t = time

SHM has many applications in physics, engineering, and other fields, including:

1. Mechanical systems
2. Electrical circuits
3. Sound waves
4. Light waves
5. Quantum mechanics