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Spring Harmonic Oscillator

A spring harmonic oscillator is a spring that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement.

The angular frequency for a spring harmonic oscillator equals the natural angular frequency, as well as 2\[Pi] times the frequency. The frequency equals the reciprocal of the period. The natural angular frequency equals the square root of the ratio between the spring constant and the mass.

Formula

{QuantityVariable["ω", "AngularFrequency"] == QuantityVariable[Subscript["ω", "0"], "AngularFrequency"], QuantityVariable[Subscript["ω", "0"], "AngularFrequency"] == Sqrt[QuantityVariable["k", "SpringConstant"]/QuantityVariable["m", "Mass"]], QuantityVariable["ω", "AngularFrequency"] == 2*Pi*QuantityVariable["f", "Frequency"], QuantityVariable["f", "Frequency"] == QuantityVariable["T", "Period"]^(-1)}

symbol description physical quantity
ω angular frequency "AngularFrequency"
ω0 natural angular frequency "AngularFrequency"
k spring constant "SpringConstant"
m mass "Mass"
f frequency "Frequency"
T period "Period"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Spring Harmonic Oscillator"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Spring Harmonic Oscillator"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Spring Harmonic Oscillator"], {QuantityVariable[ "k","SpringConstant"] -> Quantity[1, ("Newtons")/("Meters")], QuantityVariable["T","Period"] -> Quantity[1, "Seconds"]}]
Out[3]=

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