Forced Harmonic Oscillator

1
Forced Harmonic Oscillator
Solution
General solution of associated homogeneous
equation (Transient Term) (Decays to zero as t ?
?)
Particular solution of inhomogeneous
equation (Steady State Term)
2
In special case of underdamped oscillation (?2lt?0)
Transient Term
Steady State Term
? Natural frequency of free oscillation
? Frequency of damped oscillation
? ? Frequency of external
driving force
Conclusion Given enough time, oscillation
associated with natural frequency (i.e., ?0 ,?d)
dies out and the system oscillates with
frequency of external force (i.e., ?).