Simple Harmonic Motion Simple Harmonic Motion – Vibration about an equilibrium position in which the restoring force is proportional to the displacement from equilibrium. At the equilibrium position, velocity reaches a maximum. At maximum displacement, spring force and acceleration reach a maximum. The direction of the force acting on the mass (Felastic) is always opposite the direction of the mass’s displacement from equilibrium.

Hooke’s Law Restoring Force – The spring force always pushes or pulls the mass back toward its original equilibrium position. The restoring force is directly proportional to the displacement of the mass. Hooke’s Law Equation: Felastic = -kx Spring force = -(spring constant x displacement) The negative sign in the equation signifies that the direction of the spring force is always opposite the mass’s displacement.

The Simple Pendulum A simple pendulum consists of a mass called a bob, which is attached to a fixed string. The restoring force for a pendulum is a component of the bob’s weight. For small angles (< 15-20°), the pendulum’s motion is simple harmonic. In the case of a pendulum, gravitational potential energy, rather than elastic potential energy, increases as a pendulum’s displacement increases.

Types of Waves Wave – A vibration in time and space. Mechanical Wave – A wave that propagates through a deformable, elastic medium. Medium – The material through which a disturbance travels. Pulse Wave – A single, non-periodic disturbance. Periodic Wave – A wave whose source is some form of periodic motion.

Types of Waves (cont.) Transverse Wave – A wave whose particles vibrate perpendicularly to the direction of wave motion.

Types of Waves (cont.) Longitudinal Wave – A wave whose particles vibrate parallel to the direction of wave motion.

Characteristics of Waves Wave Properties: Transverse waves - Sine wave

Characteristics (cont) Crest – The highest point of a wave. Trough – The lowest point of a transverse wave. Amplitude – The greatest distance that particles in a medium move from their normal position (rest position) when a wave passes. Wavelength – The distance between any two successive identical parts of a wave. Rest Position – The position of the medium without any disturbance.

Parts of a wave Crest Wavelength Amplitude Trough Rest Position

Waves (cont) Wave Speed – The speed at which a wave passes through a medium. The units for wave speed are m/s.

Waves (cont) Period – The time required for one full wavelength Frequency – The number of vibrations that occur in a 1s time interval. The unit for frequency is Hertz (Hz). This means per second.

Wave Interactions Interference - The net effect of the combination of two or more waves. Constructive Interference – Interference between two or more waves in which amplitudes are additive and the resultant wave is larger than any of the original waves.

Wave Interactions (cont.) Destructive Interference - Interference between two or more waves in which amplitudes are subtractive and the resultant wave is smaller than any of the original waves.

Waves Interactions (cont) Doppler Effect – An observed change in the frequency of a wave when the source or observer is moving.

Wave Interactions (cont) Standing Wave – A wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere. Node – A point in a standing wave where minimum vibration occurs due to destructive interference. Antinode – A point in a standing wave where maximum vibration occurs due to constructive interference.

Wave Interactions (cont)

Wave Interactions (cont.)