Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
physical phenomenon
|
| gptkbp:displacement |
x(t)
|
| gptkbp:example |
mass-spring system
pendulum (small angles) |
| gptkbp:exhibits |
simple harmonic motion
|
| gptkbp:frequency |
f = 1/T
|
| gptkbp:hasAcceleration |
a(t) = -Aω^2 cos(ωt + φ)
|
| gptkbp:hasAmplitude |
A
|
| gptkbp:hasAngularFrequency |
ω = sqrt(k/m)
|
| gptkbp:hasApplication |
electronics
mechanics quantum mechanics |
| gptkbp:hasDamping |
none (ideal case)
|
| gptkbp:hasEnergy |
E = (1/2)kA^2
|
| gptkbp:hasEquationOfMotion |
F = -kx
|
| gptkbp:hasKineticEnergy |
K = (1/2)mv^2
|
| gptkbp:hasPhaseConstant |
φ
|
| gptkbp:hasPotentialEnergy |
U = (1/2)kx^2
|
| gptkbp:hasResonance |
at natural frequency
|
| gptkbp:hasRestoringForce |
proportional to displacement
|
| gptkbp:hasVelocity |
v(t) = -Aω sin(ωt + φ)
|
| https://www.w3.org/2000/01/rdf-schema#label |
simple harmonic oscillator
|
| gptkbp:isLinearSystem |
true
|
| gptkbp:period |
T = 2π/ω
|
| gptkbp:solvedBy |
x(t) = A cos(ωt + φ)
|
| gptkbp:studiedIn |
physics
|
| gptkbp:bfsParent |
gptkb:Ordinary_Differential_Equations
gptkb:Hamiltonian_systems |
| gptkbp:bfsLayer |
6
|