7vibrations_waves

# 7vibrations_waves - 1 Simple Harmonic Motion 2 Some...

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Unformatted text preview: 1 Simple Harmonic Motion 2 Some Oscillating Systems 3 Hooke's Law • That linear dependence of displacement upon stretching force is called Hooke's law. • According to Hooke's law, the force required to stretch the spring will be directly proportional to the amount of stretch. F = -kx 4 Hooke's Law • One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. 5 Mass on Spring: Motion Sequence • A mass on a spring will trace out a sinusoidal pattern as a function of time, as will any object vibrating in simple harmonic motion 6 7 Description of Periodic Motion • Motion which repeats itself precisely can be described with the following terms: Period: the time required to complete a full cycle, T in seconds/cycle Frequency: the number of cycles per second, f in 1/seconds or Hertz (Hz) Amplitude: the maximum displacement from equilibrium, A in meters (m) 8 Elastic Potential Energy • Elastic potential energy is Potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring. It is equal to the work done to stretch the spring. • The work done to stretch the spring a distance x is 9 Energy in Mass on Spring The simple harmonic motion of a mass on a spring is an example of an energy transformation between potential energy and kinetic energy. In the example below, it is assumed that 2 joules of work has been done to set the mass in motion. 10 11 Simple Harmonic Motion When a mass is acted upon by an elastic force which tends to bring it back to its equilibrium configuration, and when that force is proportional to the distance from equilibrium, then the object will undergo simple harmonic motion when released. equilibrium, then the object will undergo simple harmonic motion when released....
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7vibrations_waves - 1 Simple Harmonic Motion 2 Some...

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