damped harmonic motion
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DESCRIPTIONDamped Harmonic Motion. 4.3.1 State what is meant by damping. If a mass on the end of a spring is pulled down and released it will continue to oscillate until something retards it’s motion. . Damped Harmonic Motion. 4.3.1 State what is meant by damping. - PowerPoint PPT Presentation
Damped Harmonic Motion4.3.1 State what is meant by damping.If a mass on the end of a spring is pulled down and released it will continue to oscillate until something retards its motion.
1Damped Harmonic Motion
4.3.1 State what is meant by damping.Damped harmonic motion is harmonic motion with a frictional or drag force. If the damping is small, we can treat it as an envelope that modifies the undamped oscillation.
2Damped Harmonic Motion
However, if the damping is large, it no longer resembles SHM at all.A: underdamping: there are a few small oscillations before the oscillator comes to rest.
Damped Harmonic Motion
B: critical damping: this is the fastest way to get to equilibrium.C: overdamping: system comes to rest without oscillating, but does not achieve in the shortest possible time.http://www.patana.ac.th/secondary/science/anrophysics/ntopic4/commentary.htm
Damped Harmonic Motion
There are systems where damping is unwanted, such as clocks and watches.Then there are systems in which it is wanted, and often needs to be as close to critical damping as possible, such as automobile shock absorbers and earthquake protection for buildings.
ExamplesUnder-damping mass on a stiff springCritical damping door closing damper
Damped Harmonic Motion4.3.2 Describe examples of damped oscillations. Reference should be made to the degree of damping and the importance of critical damping.7Damping is caused my dissipative forces, such as air viscosity, and work is taken from the energy of oscillation.Damping is the process whereby energy is taken from the oscillating systemFor example a playground swingIf you push it will oscillateIt will eventually slow down as energy is lost to frictionEnergy needs to be supplied to keep it oscillating, that comes from you!Damped Harmonic Motion4.3.2 Describe examples of damped oscillations. Reference should be made to the degree of damping and the importance of critical damping.8Forced Vibrations; Resonance4.3.3 State what is meant by natural frequency of vibration and forced oscillations.Forced vibrations occur when there is a periodic driving force. This force may or may not have the same period as the natural frequency of the system.If the frequency is the same as the natural frequency, the amplitude becomes quite large. This is called resonance.
The oscillations so far have been free oscillations, or natural oscillations, which the system has been given some energy and left alone.The frequency of oscillation depends on the inertia and elasticity factors of the systemFor exampleGuitar string, it will always play the same notes regardless of how hard you pluck itA childs swing, it will always swing at the same rate regardless of how hard you push itThis is called the natural frequency, f0Forced Vibrations; ResonancePreviously the oscillations have been given a single push to start them movingOften oscillations are subjected to a constant force, called the driving force, fThe effect that the driving for has depends on its frequency
Forced Vibrations; ResonanceThe damping of the system has these effects:AmplitudeThe amplitude is decreases with damping (cuts down the sharp peak)The maximum amplitude is at a frequency less than the natural frequencyEnergyThe power of the driver is controlled by damping
Forced Vibrations; Resonance4.3.4 Describe graphically the variation with forced frequency of the amplitude of vibration of an object close to its natural frequency of vibration. Students should be able to describe qualitatively factors that affect the frequency response and sharpness of the curve.Wine glass demoThe glass can be forced to vibrate at its natural resonant frequency. Resonance occurs when these forced vibrations reach maximum amplitude. Microwaves natural resonant frequency of 2450 MHz. Gallstones, Kidney stonesTacoma Narrows Bridge, Troops MarchingQuartz Oscillators-A quartz feels a force if placed in an electric field and will oscillate when removed. -Appropriate electronics are added to generate an oscillating voltage from the mechanical movements of the crystal and this is used to drive the crystal at its own natural frequency.-These devices provide accurate clocks for microprocessor systems.Musical Instruments-Produce their sounds by arranging for column of air or a string to be driven at its natural frequency, which causes the amplitude of the oscillations to increase.4.3.6 Describe examples of resonance where the effect is useful and where it should be avoided. Applications of ResonanceResonance occurs when the an oscillator is acted upon by a driving force that has the same frequency as the natural frequencyThe driving force easily transfers its energy to the oscillatorFrom the picture the amplitude of oscillation will become very highThis can be a useful and sometimes very bad
Forced Vibrations; Resonance4.3.5 State what is meant by resonance. Electricity, tuning a radioThe natural frequency of the radio circuit is made equal to the incoming electromagnetic wave by changing its capacitanceThe electrons in the circuit will oscillate with the incoming electromagnetic wave.The electric current will oscillate and this can be turned into sound, through a speakerMicrowave ovensMicrowaves are produced at the same frequency as the natural frequency of water moleculesWater molecules absorb the energy from the microwaves and transfer their energy to the food in the form of thermal energyApplications of ResonanceA Driving force at resonance increases the oscillations, sometimes this is unwantedStructuresTacoma Narrows bridge, this bridge was destroyed as the wind (driving force) was at the same as the natural frequency. The bridge vibrated and shook itself apartApplications of Resonance
An additional unwanted resonance would beTower blocks, the same effect as the bridge the wind, or earthquakes, can cause vibrations to destroy the buildingsVibrations in machinery, if the driving force equals the natural frequency the amplitude may get dangerously high. Ex. At a particular speed in a trucks rear view mirror can be seen to vibrateThis can be stopped by designing the building with heavy dampingHigh stiffnessLarge massShapeGood at absorbing energyApplications of ResonanceThe simple harmonic motion of a mass on a spring is an example of an energy transformation between potential energy and kinetic energy.
Energy in the Simple Harmonic Oscillator4.2.1 Describe the interchange between kinetic energy and potential energy during SHM.Potential Energy
At extension x:
Energy in the Simple Harmonic Oscillator4.2.2 Apply the expressions Ek=1/2 m2 (xo2-x2) for the kinetic energy of a particle undergoing SHM, ET=1/2 m2xo2 for the total energy and EP=1/2 m2x2 for the potential energy.Kinetic EnergyAt extension x:
Energy in the Simple Harmonic Oscillator
Total energyTotal energy
Energy in the Simple Harmonic Oscillator4.2.3 Solve problems, both graphically and by calculation, involving energy changes during SHM.