CSimple Harmonic Motion and Waves
Kinematics of simple harmonic motion:
Oscillation: an effect expressible as a quantity that repeatedly and regularly fluctuates above and below a average value, as the pressure of an alternating current. Examples include: • Cycle: One cycle is defined as one complete oscillation of the pendulum (A-B-A) • Equilibrium Position: the position where the pendulum would be at rest when undisturbed (O) • Amplitude (x0): maximum displacement from equilibrium position (OB or OA) – measured in metres. • Time Period (T): the length of time to complete one cycle – measured in seconds • Frequency (f): the number of cycles the pendulum makes per unit time – measured in 1/s or hertz (Hz) • Angular frequency (ω or 2πf): used when describing circular motion, or even an oscillation in the case of 2π equivalent to one cycle. Displacement: the distance of an oscillating body from its central position or point of equilibrium at any given moment. Amplitude: the absolute value of the maximum displacement from a zero value during one period of an oscillation. Frequency: the number of periods or regularly occurring events of any given kind in unit of time. This is usually measured in one second. Period: the time taken to complete one cycle of a regularly recurring phenomenon Phase Difference:
Simple Harmonic Motion: vibratory motion in a system in which the restoring force is proportional to the displacement from equilibrium. This is expressed by the equation: a = -ω^2x
Energy changes during simple harmonic motion (SHM):
Kinetic energy = mv^2 /2 and the potential energy at any point = total energy – KE. Because no energy is lost when the total energy is a constant value, the energy when a body is active sees continual changes between kinetic and potential energy.
Forced oscillations and resonance:
Damping: The effect in which there is a loss of energy due to the friction in real oscillation....
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