Cantareath
. How does the period of time of damped
Oscillation depend on the damping coefficient?
Answers
Answer:
In case of forced oscillations, period of oscillation does not depend on the damping force and is equal to frequency of driving force. The damping force only reduces the amplitude of oscillation at resonance and creates a lagging response. If the driving force is suddenly switched off at resonant frequency , the oscillation amplitude will decay exponentially at the oscillation frequency less than resonant frequency due to the damping effect . On further increasing the damping constant above a critical value oscillation stops completely and response becomes purely exponentially decaying. System is then called critically damped. Such transition from oscillatory response to exponential hints at the deeper connection between cosine and exponential functions. No wonder why complex number aided by remarkable Euler's formula acts as two way bridge between these functions and facilitates an easy mathematical solution to oscillation problems. The differentiation operation is reduced to ordinary multiplication operation by use of complex exponential functions.