Plz. Explain damped oscillation with the equation related.
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?
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.