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Periodic MotionMotions that repeat in a regular

cycle.

Simple Harmonic Motion

- During motion, object has one point where the net

force is zero (equilibrium). - Whenever the object if pulled away from

equilibrium, the net force becomes non-zero and

works to pull the object back to equilibrium. - The force needed to restore equilibrium is

directly proportional to the displacement of the

object.

- Period (T) - time for the object to complete one

cycle of motion. - Amplitude - maximum distance that the object

moves away from equilibrium.

- Hookes Law - The force exerted by a spring is

equal to the spring constant times the distance

the spring is compressed or stretched from its

equilibrium point. F -kx - Potential energy in a stretched or compressed

spring is equal to one half the product of the

spring constant and the square of the

displacement. PEsp ½ kx2

Period of a Pendulum is equal to two times pi

times the square root of the length of the

pendulum divided by acceleration due to gravity.

T 2?vl/g

Resonance - the increase in the amplitude of a

vibrating or oscillating object due to the

application of small forces during regular

intervals.

- Pumping your legs when swinging.
- Wind causing the Tacoma Narrows bridge collapse.

Wave - a disturbance that carries energy through

matter or space (matter is not transferred).

- Transverse Wave - wave pulse (disturbance)

vibrates perpendicular to the direction of the

waves motion. - Longitudinal Wave - wave pulse (disturbance)

vibrates parallel to the direction of the waves

motion.

Wave Measurements

- Speed (v) - the speed of a wave pulse is equal to

the displacement of the wave peak divided by the

amount of time. v ?d / ?t - Amplitude (A) - the maximum displacement of the

wave from its position of rest. For waves that

have the same speed, the rate of energy transfer

is proportional to the square of the amplitude. - Wavelength (?) - the shortest distance between

points where the wave pattern repeats itself. - Period (T) - the time it takes wave to complete

one cycle (wavelength). - Frequency (f) - the number of complete

oscillations it makes each second.

- The frequency of a wave is equal to the

reciprocal of the period. f 1 / T - The wavelength is equal to velocity divided by

the frequency. ? v / f

Wave Behavior

- Incident wave - initial wave that strikes a

boundary. - Reflected wave - returning wave after the

collision of the incident wave with a boundary.

Principle of Superposition

- When two waves exist in the same place in the

medium at the same time the displacement of the

medium is equal to sum of the two individual wave

displacements.

Wave Interference - the result of the

superposition of two or more waves.

- Destructive - when two waves with opposite

amplitudes meet. If these are equal amplitudes

then the point that they meet (node) does not

move. - Constructive - when two waves with amplitudes in

the same direction meet. Produces an a point

where the largest amount of displacement occurs

(antinode).

- Standing waves are produced through the

constructive and destructive interference of

waves. Increasing the frequency of oscillations

increases the number of nodes and antinodes.

Waves in 2 Dimensions

- When an incident wave strikes a barrier it will

be reflected. The angles formed between the

incident ray and the normal (draw line that is

perpendicular to the barrier) and the reflected

ray and the normal are equal.

- Refraction is the change in direction of a wave

at the boundary between two different media. - For example waves approaching shore will always

have the same frequency, however, their

wavelength and velocity decreases. This will

cause a change in direction between these two

media.