Simple harmonic oscillator

URI: https://gptkb.org/entity/Simple_harmonic_oscillator
GPTKB entity
Statements (51)
Predicate Object
gptkbp:instanceOf Physical system
gptkbp:displacement x
gptkbp:example Mass-spring system
Simple pendulum (small angles)
gptkbp:frequency f = 1/T
gptkbp:hasAcceleration a = -Aω^2 cos(ωt + φ)
gptkbp:hasAmplitude A
gptkbp:hasAngularFrequency ω = sqrt(k/m)
gptkbp:hasDamping No (ideal case)
gptkbp:hasEnergyConservation True (ideal case)
gptkbp:hasEquationOfMotion d2x/dt2 + ω^2 x = 0
gptkbp:hasGraph Sinusoidal
gptkbp:hasMaximumAcceleration a = ±Aω^2
gptkbp:hasMaximumDisplacement x = ±A
gptkbp:hasMaximumForce F = ±kA
gptkbp:hasMaximumKineticEnergy K = (1/2)kA^2 at x = 0
gptkbp:hasMaximumNetForceAt x = ±A
gptkbp:hasMaximumPotentialEnergy U = (1/2)kA^2 at x = ±A
gptkbp:hasMaximumVelocity v = ±Aω
gptkbp:hasMinimumKineticEnergy K = 0 at x = ±A
gptkbp:hasMinimumPotentialEnergy U = 0 at x = 0
gptkbp:hasNoNetForceAt x = 0
gptkbp:hasPhaseConstant φ
gptkbp:hasPhaseDifferenceBetweenDisplacementAndAcceleration π
gptkbp:hasPhaseDifferenceBetweenDisplacementAndVelocity π/2
gptkbp:hasPhaseDifferenceBetweenVelocityAndAcceleration π/2
gptkbp:hasPotentialEnergy U = (1/2) k x^2
gptkbp:hasQuantumVersion Quantum harmonic oscillator
gptkbp:hasResonance No (undriven case)
gptkbp:hasRestoringForce F = -kx
gptkbp:hasRestoringForceDirection Opposite to displacement
gptkbp:hasRestoringForceProportionalToDisplacement True
gptkbp:hasRestPosition x = 0
gptkbp:hasTotalEnergy E = (1/2) k A^2
gptkbp:hasUnitsOfAcceleration m/s^2
gptkbp:hasUnitsOfAmplitude m
gptkbp:hasUnitsOfAngularFrequency rad/s
gptkbp:hasUnitsOfDisplacement m
gptkbp:hasUnitsOfEnergy gptkb:Joule
gptkbp:hasUnitsOfForce gptkb:Newton
gptkbp:hasUnitsOfFrequency Hz
gptkbp:hasUnitsOfMass kg
gptkbp:hasUnitsOfSpringConstant N/m
gptkbp:hasUnitsOfVelocity m/s
gptkbp:hasVelocity v = -Aω sin(ωt + φ)
https://www.w3.org/2000/01/rdf-schema#label Simple harmonic oscillator
gptkbp:period T = 2π/ω
gptkbp:solvedBy x(t) = A cos(ωt + φ)
gptkbp:studiedIn gptkb:Physics
gptkbp:bfsParent gptkb:Sine_function
gptkbp:bfsLayer 8