Harmonic oscillator is a second order derivative equation¶
In classical mechanics a simple harmonic oscillator is a system that, after a small displacement from equilibrium, experiences a restoring force \(F\) proportional to that displacement. Displacement is not only limited to physical motion, but should be interpreted in general terms. Examples include small-angle pendulums, mass–spring systems, acoustic resonators, and electrical RLC circuits. If \(F\) is the only force acting on the system, the system is called a simple harmonic oscillator.
Conditions:
There is no damping (i.e. friction) in the system.
The system experiences a single restoring force \(F\) (for mechanical oscillators).
Links:
- Symbol:
t- Latex:
\(t\)
- Dimension:
time
- displacement¶
Displacement of oscillator from equilibrium as a function of time. See
any_quantity.
- Symbol:
x(t)- Latex:
\(x{\left(t \right)}\)
- Dimension:
any_dimension
- angular_frequency¶
angular_frequencyof the oscillator.
- Symbol:
w- Latex:
\(\omega\)
- Dimension:
angle/time
- definition¶
Derivative(x(t), (t, 2)) = -w^2 * x(t)- Latex:
- \[\frac{d^{2}}{d t^{2}} x{\left(t \right)} = - \omega^{2} x{\left(t \right)}\]