Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium position. This motion is characterized by a restoring force that is directly proportional to the displacement from the equilibrium position.
The formula for simple harmonic motion is x(t) = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle.
The period of oscillation, represented by the symbol T, is the time it takes for one complete cycle of the oscillating motion. It can be calculated using the formula T = 2π/ω, where ω is the angular frequency.
The period of simple harmonic motion is affected by two main factors: the mass of the object and the stiffness of the restoring force. As the mass increases, the period also increases. Similarly, as the stiffness of the restoring force increases, the period decreases.
The frequency, represented by the symbol f, is the number of cycles per unit time. It is inversely proportional to the period, meaning that as the frequency increases, the period decreases. This relationship can be expressed as f = 1/T.