Periodic Motion

Periodic Motion

Periodic Motion

periodic motion: are motions, which all repeat in a regular cycle

In each periodic motion, the object has one position at which the net force on it is zero. At that position, the object is in equilibrium.

Whenever the object is pulled away from its equilibrium position, the net force on the system becomes nonzero and pulls the object back toward equilibrium

Pendulums

Simple harmonic motion also can be demonstrated by the swing of a pendulum

A simple pendulum consists of a massive object, called the bob, suspended by a string or light rod of length l

The string or rod exerts a tension force, FT, and gravity exerts a force, Fg, on the bob.

The vector sum of the two forces produces the net force, shown at three positions in the adjoining figure.

Resonance

It occurs when small forces are applied at regular intervals to a vibrating or oscillating object and the amplitude of the vibration increases.

The time interval between applications of the force is equal to the period of oscillation.

Waves

New Vocabulary Wave Wave pulse Transverse wave Surface wave Trough Crest Wavelength Frequency Longitudinal wave

A wave is a disturbance that carries energy through matter or space.

Waves transfer energy without transferring matter

Type of waves according to need a medium to travel

1) Mechanical waves require a medium, such as water wave, air wave, ropes wave, or a spring. sound wave

2) Electromagnetic waves: waves not require medium. Light waves, TV waves, X-ray…..

A wave pulse is a single bump or disturbance that travels through a medium.

Types of waves according to pulse direction

1- A transverse wave is one that vibrates perpendicular to the direction of the wave’s motion Ex. Light waves, rope waves

2- longitudinal wave: The disturbance is in the same direction as, or parallel to, the direction of the wave’s motion

Sound waves are longitudinal waves. Fluids usually transmit only longitudinal waves.

3- a surface wave, which has characteristics of both transverse and longitudinal waves.

Waves that are deep in a lake or ocean are longitudinal; at the surface of the water, however, the particles move in a direction that is both parallel and perpendicular to the direction of wave motion, as shown in the figure below

Describing a wave

There are many ways to describe or measure a wave. Some characteristics depend on how the wave is produced, whereas others depend on the medium through which the wave travels.

1. Speed: how fast does wave move, depends only on the medium through which the waves move.

2. Amplitude: the maximum displacement of the wave from its position of rest or equilibrium

wave’s amplitude depends on how it is generated, but not on its speed.

Waves with greater amplitudes transfer more energy ( E α A2 )

Describing a wave

( energy transferred α A2)

EX: Thus, doubling the amplitude of a wave increases the amount of energy it transfers each second by a factor of 4

** trough : each low point of a wave

** crest : Each high point of a wave

Describing a wave

3. Wavelength ( λ ): The shortest distance between points where the wave pattern repeats itself

Depend on : a) frequency ( source) b) speed ( medium)

4. Phase: used to describe the position of a point in a wave

In phase: Any two points in wave separated by (λ, 2 λ, 3 λ,…..) OR ( 0, 2π, 4 π,……)

Particles in the medium are said to be in phase with one another when they have the same displacement from equilibrium and the same velocity

Out of phase : Any two points in wave separated by (λ/2, 2 λ/2, 3 λ/2,…..) OR ( π, 3 π,5 π ,……)

Particles in the medium with opposite displacements and velocities are out of phase

Describing a wave

5. Period( T ) : time it takes the source to complete one cycle.

OR : Time taken by a point on wave to return to its initial phase

6. Frequency ( f ): number of complete oscillation( waves) in one second

Describing a wave

1. Both the period and the frequency of a wave depend only on its source. They do not depend on the wave’s speed or the medium

2. period of wave = period of source

Important Notes About Period And Frequency

The wavelength of a wave is equal to the velocity divided by the frequency.

Important Notes About Period And Frequency

Q1: In fig1, if the total time is 0.2sec, find the wave length, period, frequency, speed, and amplitude .(#of waves is2.5

Q2: In fig1, find the period, frequency, and amplitude . If the wave length is 3m, what is the speed of the wave?

Q: Distinguish between transverse waves and longitudinal waves.

1. Transverse Wave Longitudinal Wave 1. A transverse wave is one that vibrates

perpendicular to the direction of the wave’s motion.

2. A quick shake of a rope sends transverse waves in both directions.

3. Waves obtained in threads and ropes are transverse waves.

1. A longitudinal wave is one in which the particle displacement is in the same direction as, or parallel to, the direction of the wave’s motion.

2. The squeeze and release of a coiled-spring toy sends out longitudinal wave pulses in both directions.

3. Waves obtained in springs and sounds are longitudinal waves.