Simple Harmonic Motion and Waves

Simple Harmonic Motion and Waves

Lecture #2

Air Resistance and Internal and External Friction Bring SHM to a stop.

Damped Harmonic Motion

Damped Harmonic Motion

Overdamped — Curve A—damping is so large it takes a LONG time to reach equil.

Underdamped —Curve C—the system makes several swings before coming to rest

Critical Damping —Curve B —equilibrium is reached the quickest

Damped Harmonic Motion

Objects (matter) tends to vibration a certain natural frequency. (fo) (also known as resonant frequency)

Forced vibration occurs when a repeated external force is applied to a vibrating system that has its own particular frequency. ( f )

Forced Vibrations and Resonance

Forced Vibrations and Resonance

For a forced system, Amplitude depends on the difference between f and fo

Maximum amplitude is reached when f = fo

This can have some Stunning implications.

Forced Vibrations and Resonance

Forced Vibrations and Resonance

Wave Motion

Particle Velocity – the particles oscillate about a fixed point

Wave Velocity – the velocity of the wave is in the direction of the wave

Wave Motion

Pulse – one bump Continuous Wave – wave from a source that

is oscillating

Wave Motion - Terms

Transverse – Particle Motion is perpendicular to Wave Motion

Longitudinal – Particle Motion is parallel to Wave Motion

Wave Motion - Types

MISCONCEPTION ALERT In BOTH types of waves, the particle

oscillates about a point.

Wave Motion - Types

Wave Motion – critical formulas Wave Velocity = wavelength multiplied by

the frequency

T is often easier to find. T = 1/f

Velocity of a wave in a “string” is equal to the square root of:

The tension force in the string divided by the mass over length (not density)

Wave Motion - critical formulas