Oscillation Flashcards
Oscillation
a repetitive back and forth or up and down motion
Natural frequency
the frequency at which a body vibrates when there is no (resultant external) resistive force acting on it
Sinusoidal
having the form of a sine curve
Amplitude
the amplitude of a vibration is the maximum displacement of a particle from its equilibrium position
Period
the period of an oscillating system is the time taken to make one complete oscillation
Phase
the point that an oscillating particle has reached within the complete cycle of an oscillation
Phase difference
the difference in the phases of oscillating particles measured in degrees or radians
Simple harmonic motion
a body executes a simple harmonic if its acceleration is directly proportional to its displacement from its equilibrium position, and in the opposite direction to its displacement
Angular frequency
the frequency of a sinusoidal oscillation expressed in radians per second
Relationship between angular frequency and frequency
ω = 2πf
Equations of simple harmonic motion
x = x₀sinωt
x = x₀cosωt
Acceleration of an object vibrating in simple harmonic motion
a = –ω²x
Key idea behind acceleration of an object vibrating in simple harmonic motion
We say that the equation a = –ω²x defines simple harmonic motion, it tells us what is required if a body is to perform s.h.m.
The equation x = x₀sinωt is then described as a solution to the equation, since it tells us how the displacement of the body varies with time
Total energy of a system undergoing simple harmonic motion
E₀ = 1/2mω²x₀²
Damped
a damped oscillation is an oscillation in which resistive forces cause the energy of the system to be transferred to the surroundings as internal energy
