Terms and Formulae
Terms
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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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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