Simple Harmonic Motion and Waves SL

Published on January 2017 | Categories: Documents | Downloads: 55 | Comments: 0 | Views: 219
of 7
Download PDF   Embed   Report

Comments

Content

Simple Harmonic Motion and Waves SL

Simple Harmonic Motion Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. (Wikipedia: Simple harmonic motion) 4.1.1: Describe Examples of Oscillations Oscillation is the repetitive variation, typically in time of some measure about a point of equilibrium. The motion of a mass at the end of a string after it is displaced from its equilibrium position. The motion of a ball after inside a bowl after it has been displaced from equilibrium.

-

4.1.2: Define the terms displacement, amplitude, frequency, period and phase difference. Cycle: One completed oscillation of a pendulum, or one complete circle (2π radians) Amplitude (X0): The maximum displacement from the equilibrium position. It is the maximum extent of an oscillation. Equilibrium (O): The position in which the bob will rest if not disturbed. Displacement: Distance moved from equilibrium. Frequency (f): The number of cycles per unit time, measured by 1/time. Unit: Hertz (Hz) or s-1.

Angular frequency (ω): A scalar measure of rotation rate. This is used to describe circular motion. Angular frequency is found by multiplying f with 2π, measured in radians per second (rad s-1).

Period: time taken to complete one full oscillation. This is the time taken to move from one extreme position and back to the same position.



Simple Harmonic Motion and Waves SL

4.1.3: Define simple harmonic motion (SHM) and state the defining equation as a = −ω2x . Simple Harmonic motion (SHM): This when the oscillation’s restoring force is directly proportional to displacement, meaning that the acceleration is proportional to the distance from a fixed point, and is always directed towards it.

4.1.5: Apply the equations of velocity, displacement, and period of SHM. Displacement: Velocity: Acceleration: Circular motion can also be simple harmonic motion. Centripetal acceleration:: Acceleration: Velocity: Maximum velocity: 4.2.1: Describe the interchange between kinetic energy and potential energy during SHM At the top of the swing, the mass has maximum potential energy, and minimum kinetic energy. At the bottom, it has maximum kinetic energy, and minimum potential energy. √

For graphical analysis Derived from the velocity formula

Simple Harmonic Motion and Waves SL

Derived from total energy - KE

For graphical analysis

Given the maximum potential energy, the period of an oscillation can be calculated using:

The maximum speed (speed past equilibrium) can be found using:

It can also be found by rearranging the following formula:

For a mass resting on an oscillating surface, Net force is equal to:

This can be rearranged to find the amplitude. The normal force can also be calculated.

4.3.1: State what is meant by damping Damped oscillations are those that occur in the presence of resistive forces. Damping is the loss of energy, as a system has to do work against the resistive forces. Critical damping occurs when the resistive forces are big enough to bring the mass to equilibrium without passing through it.

Simple Harmonic Motion and Waves SL

4.3.3: State what is meant by natural frequency of vibration and forced oscillations Natural frequency: the frequency at which a system tends to oscillate in the absence of any driving or damping force. (Wikipedia: Natural Frequency). A forced oscillation is one where the system is forced to oscillate at a different frequency. When the driving frequency equals the natural frequency, resonance occurs, resulting in oscillations with a large amplitude. The amplitude of an oscillation against the driving frequency is called a resonance curve. The sharpness is affected by the amount of damping in the system. Phase difference is the difference, expressed in electrical degrees or time, between two waves having the same frequency and referenced to the same point in time. Two oscillators that have the same frequency and no phase difference are said to be in phase. Two oscillators that have the same frequency and different phases have a phase difference, and the oscillators are said to be out of phase with each other. 4.4.1: Describe a wave pulse and a continuous progressive (traveling) wave A wave is a disturbance that transfers energy and momentum from one place to another through a medium. Transverse waves: waves in which the disturbance is at right angles to the direction of energy transfer. Longitudinal waves: waves in which the disturbance is along the direction of energy transfer. A wave pulse is a disturbance that you can see travel from one end to another. A travelling wave is found by producing one pulse after another. These waves distribute energy from a point source to a surrounding area. They move energy in the form of vibrating particles or fields. (S-cool: Progressive waves)

Simple Harmonic Motion and Waves SL Wavelength (λ): The distance over which the wave's shape repeats (Wikipedia: Wavelength) This can be found from a displacement-position graph. Period (T): The time needed to produce a full wave. This can be found from a displacement-time graph.

Wave speed (v): the distance traveled by the wave profile per unit time.

Frequency (f): Number of complete cycles that pass a point per unit time.

Amplitude (A): The maximum displacement of the wave from the equilibrium position. Crest: Position on a wave with maximum displacement. Trough: Position on a wave with minimum displacement.

Wavefront: line joining points that are in phase. Circular wavefronts are produced by point disturbances, while plane wavefronts are produced by extended disturbance. As a wave moves away from the point of impact, the length of the wavefronts increases as the energy per unit wavefront length decreases. 4.5.1: Describe the reflection and transmission of waves at a boundary between two media. When a wave hits a barrier, it is reflected. For example, a pulse would exert an upwards forced on the barrier. In turn, the barrier would exert and equal and opposite force on the pulse, inverting it and making it travel towards the left. The laws of reflection: Angles of incidence = angle of reflection. The incident and reflected rays are in the same plane as the normal.

Simple Harmonic Motion and Waves SL

4.5.2: State and Apply Snell’s law Refraction: Due to change of medium, the phase velocity of a wave is changed but its frequency remains constant (Wikipedia: Refraction) Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, for waves passing through a boundary between two different mediums. (Wikipedia: Snell’s Law)

The ratio of the velocity of light in two different media is called the refractive index. Rays with the same angle of incidence but a different wavelength are refracted by different angles. Since the frequency does not change, the waves have a shorter wavelength in regions of lower wave speeds. In this case, the direction of the wave bends towards the normal. 4.5.4: Describe examples of diffraction Diffraction: the apparent bending of waves around small obstacles and the spreading out of waves past small openings (Wikipedia: Diffraction) This occurs whenever the wavelength is comparable to or bigger than the aperture. It also occurs when a wave moves past an obstacle, provided the obstacle size is comparable to the wavelength.

Simple Harmonic Motion and Waves SL

4.5.5: State the principle of superposition and explain what is meant by constructive interference and by destructive interference The principle of superposition states that when two pulses meet, the displacement at that point is the algebraic sum of the individual displacements. Interference is a phenomenon in which two waves superimpose to form a resultant wave of greater or lower amplitude (Wikipedia: Interference) When waves interfere, the phase difference between the waves is different at different points. If the path difference is a whole number of wavelengths, then the waves are in phase. This is constructive interference. If the path difference is an odd number of wavelengths, then the waves are out of phase. This is destructive interference.

Sponsor Documents

Or use your account on DocShare.tips

Hide

Forgot your password?

Or register your new account on DocShare.tips

Hide

Lost your password? Please enter your email address. You will receive a link to create a new password.

Back to log-in

Close