Question
Fri March 04, 2011 By: Garima Srivastava

Plz. Explain damped oscillation with the equation related.

Expert Reply
Mon March 07, 2011
Dear student,
 
An oscillator is anything that has a rythmic periodic response. A damped oscillator has a response that fades away over time. Examples include a swinging pendulum, a bobbing weight on a spring, and also a resistor - inductor - capacitor (RLC) circuit.

Equations

Suppose you have an RLC circuit, which has a resistor + inductor + capacitor in series. When the switch closes at time t=0 the capacitor will discharge into a series resistor and inductor.

What is the voltage V and current I as a function of time?
Answer:
    

where:
   

and V= initial voltage
C = capacitance (farads)
R = resistance (ohms)
L = inductance (henrys)
e = base of natural log (2.71828...)

What Does This Mean?

The above equation is the current for a damped sine wave. It represents a sine wave of maximum amplitude (V/BL) multiplied by a damping factor of an exponential decay. The resulting time variation is an oscillation bounded by a decaying envelope.

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