Driven oscillation, also known as forced oscillation, refers to the motion of a particle or system that is continuously driven by an external force. This force can be periodic or non-periodic, and can cause the particle to oscillate with a specific frequency, amplitude, and phase.
The equation for driven oscillation is typically written as:
m(d^2x/dt^2) + γ(dx/dt) + kx = F(t)
where m is the mass of the particle, γ is the damping coefficient, k is the spring constant, and F(t) is the external force acting on the particle. This equation is known as the driven harmonic oscillator equation.
Simple harmonic motion refers to the motion of a particle or system that is driven by a restoring force (such as a spring) and is not affected by any external forces. In contrast, driven oscillation involves an external force that continuously acts on the particle, causing it to oscillate with a specific frequency and amplitude.
Driven oscillation has various applications in physics and engineering. It is commonly used in the study of mechanical systems, such as mass-spring systems and pendulums. It also has applications in electrical circuits, where it can be used to model the behavior of capacitors and inductors.
The behavior of a driven oscillating system can be analyzed using techniques such as Fourier analysis and the method of undetermined coefficients. These methods allow us to determine the frequency, amplitude, and phase of the oscillations, as well as how the system responds to different external forces.