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Forced Harmonic Oscillator

k. F 0 cos t. m. b. 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). In special case of underdamped oscillation (  2 <  0 ).

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Forced Harmonic Oscillator

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  1. k F0cost m b 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 (2<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., ).

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