Simple Harmonic Motion (SHM) is a type of periodic motion in which an object oscillates back and forth around an equilibrium point with a constant amplitude and period. It is a result of a restoring force that is proportional to the displacement of the object from its equilibrium position.
The key characteristics of SHM include a constant amplitude, a constant period, and a sinusoidal displacement graph. The motion also follows the principle of superposition, where the total displacement is the sum of two or more individual displacements.
Some real-life examples of SHM include the motion of a pendulum, a mass on a spring, the vibration of a guitar string, and the motion of a swing. These systems exhibit SHM because they have a restoring force and a stable equilibrium point.
The equation for SHM is x = A sin(ωt + φ), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle. This equation can also be written as x = A cos(ωt + φ) or x = A sin(2πft + φ), where f is the frequency in hertz.
In SHM, the total mechanical energy (potential energy + kinetic energy) of the system is constant. As the object oscillates, the energy is constantly being converted between potential and kinetic. At the equilibrium point, all of the energy is potential, and at the maximum displacement, all of the energy is kinetic. This is known as the law of conservation of energy.