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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.)