A forced harmonic oscillator is a system that undergoes periodic motion under the influence of an external force. This type of oscillator follows the laws of harmonic motion, where the restoring force is directly proportional to the displacement from equilibrium, but is also affected by an external force.
To find the general solution of motion for a forced harmonic oscillator, you need to use the differential equation that describes the motion of the oscillator. This equation can be solved using various methods, such as the method of undetermined coefficients or the Laplace transform, to obtain the general solution.
The motion of a forced harmonic oscillator can be affected by several factors, including the frequency and amplitude of the external force, the mass and stiffness of the oscillator, and any damping present in the system. These factors can alter the amplitude, frequency, and phase of the motion of the oscillator.
One example of a forced harmonic oscillator is a child's swing. The child provides a periodic external force by pumping their legs, while the swing itself follows the laws of harmonic motion. The motion of the swing can also be affected by the child's weight, the length of the swing, and air resistance.
A forced harmonic oscillator is different from a simple harmonic oscillator because it is affected by an external force, while a simple harmonic oscillator only follows the laws of harmonic motion. This external force can change the amplitude, frequency, and phase of the motion of the oscillator, making it more complex to analyze than a simple harmonic oscillator.