Damped Oscillations Having One Degree of Freedom
A damped oscillation of a system with one degree of freedom refers to the behavior of a simple system with one moving part subject to a linear viscous damping force. The system is assumed to have a small velocity, and the damping force is proportional to the velocity. The system’s motion can be described by a differential equation known as the damped harmonic oscillator equation, which can be solved to find the displacement and velocity of the system as a function of time.
d²x/dt² = -(k/m)x – (b/m)dx/dt
This equation is for small displacements and velocities. The equation can be rewritten to:
md²x/dt² +ω02x(t) +2μ.dx/dt=0
The system’s behavior depends on the character of the roots of the equation, which may be real or complex. The damping present in the system can be characterized by the quantity gamma, which has the dimension of frequency, and the constant ω0 represents the natural angular frequency of the system in the absence of damping. The system’s behavior can be heavily, weakly, or critically damped, depending on gamma values and ω0.
Damped Oscillation – Definition, Equation, Types, Examples
Damped Oscillation means the oscillating system experiences a damping force, causing its energy to decrease gradually. The level of damping affects the frequency and period of the oscillations, with very large damping causing the system to slowly move toward equilibrium without oscillating.
In this article, we will look into damped oscillation, damped oscillator, damping force, general equation derivation, application and type of damped oscillation, etc.
Table of Content
- What is Damped Oscillation?
- Damped Oscillation Differential Equation
- Damped Harmonic Oscillator
- Types of Damped Oscillator
- Effects of Damping
- Damped Oscillation Example