Terms and Formulae
Terms
Oscillating system
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Any system that always experiences a force acting against the
displacement of
the system (restoring force).
Restoring force
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A force that always acts against the displacement of the system.
Periodic Motion
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Any motion in which a system returns to its initial position at a later
time.
Amplitude
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The maximum displacement of an oscillating system.
Period
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The time it takes for a system to complete one oscillation.
Frequency
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The rate at which a system completes an oscillation.
Hertz
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The unit of measurement of frequency.
Angular Frequency
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The radian measure of frequency: frequency times 2π.
Simple Harmonic Motion
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Any motion that experiences a restoring force proportional to the
displacement of the system.
Torsional Oscillator
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The oscillation of any object suspended by a wire and rotating about
the axis of the wire.
Pendulum
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The classic pendulum consists of a particle suspended from a light
cord. When the particle is pulled to one side and released, it swings
back past the equilibrium point and oscillates between two maximum
angular displacements.
Damping force
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A force proportional to the velocity of the object that causes it to
slow down.
Resonance
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The phenomena in which a driving force causes a rapid increase in the
amplitude of
oscillation of a system.
Resonant Frequency
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The frequency at which a driving force will produce resonance in a given oscillating
system.
Formulae
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Relation between variables of oscillation
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ω = 2πν =
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Force exerted by a spring with constant k
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F = - kx
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Differential equation describing simple harmonic motion
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+ x = 0
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Formula for the period of a mass-spring system
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T = 2π
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Formula for the frequency of a mass-spring system
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ν =
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Formula for the angular frequency of a mass-spring system
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ω =
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Equation for the displacement in simple harmonic motion
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x = xmcos(ωt)
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Equation for the velocity in simple harmonic motion
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v = ωxmsin(ωt)
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Equation for the acceleration in simple harmonic motion
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a = ω2xmcos(ωt)
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Equation for the potential
energy of a
simple
harmonic system
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U = kx2
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Equation for the torque felt in a torsional oscillator
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τ = - κω
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Equation for angular displacement of a torsional oscillator
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θ = θmcos(ωt)
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Equation for the period of a torsional oscillator
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T = 2π
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Equation for the angular frequency of a torsional oscillator
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ω =
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Equation for the force felt by a pendulum
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F = mg sinθ
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Approximation of the force felt by a pendulum
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F - ()x
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Equation for the period of a pendulum
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T = 2π
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Differential equation describing damped motion
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kx + b + m = 0
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Equation for the displacement of a damped system
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x = xmecos(ω′t)
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Equation for the angular frequency of a damped system
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ω′ =
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