Simple Harmonic Motion (SHM) is a type of periodic motion in which an object oscillates back and forth around a central equilibrium point, with a constant amplitude and period. It occurs when a restoring force (such as gravity or a spring) is proportional to displacement from the equilibrium point.
The period of a SHM oscillation is affected by two main factors: the mass of the object and the strength of the restoring force. A larger mass will result in a longer period, while a stronger restoring force will result in a shorter period.
SHM is a type of harmonic motion, which is any type of motion that can be described by a sinusoidal function. The motion is considered "simple" because it follows a predictable pattern and can be described by a single frequency.
The equation for SHM is x(t) = A*cos(ωt + φ), where x is the displacement from the equilibrium point, A is the amplitude, ω is the angular frequency, and φ is the phase angle. This equation can also be written as x(t) = A*sin(ωt + φ) or x(t) = A*sin(2πft + φ), where f is the frequency in Hz.
Examples of SHM in everyday life include the swinging of a pendulum, the motion of a mass on a spring, and the vibration of a guitar string. Other examples include the motion of a bouncing ball, the swinging of a child on a swing, and the motion of a mass attached to a rubber band. SHM is also present in many natural phenomena, such as the tides and the Earth's vibrations during an earthquake.