Harmonic oscillator is a second order derivative equation¶
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x. If F is the only force acting on the system, the system is called a simple harmonic oscillator. Displacement is not only limited to physical motion, but should be interpreted in general terms. Harmonic oscillator can represent mechanical systems that include pendulums (with small angles of displacement), masses connected to springs, and acoustical systems. Other analogous systems include electrical harmonic oscillators such as RLC circuits.
Conditions:
There is no damping (i.e. friction) in the system.
Links:
- 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_frequency
of the oscillator.- Symbol:
w
- Latex:
\(\omega\)
- Dimension:
angle/time
- definition¶
Derivative(x(t), (t, 2)) = -w^2 * x(t)
- Latex:
- \[\frac{d^{2}}{d t^{2}} x{\left(t \right)} = - \omega^{2} x{\left(t \right)}\]