Question 5.12: Characterize the composite waveform obtained by multiplying ......

In this case the composite waveform is expressed as

υ(t) = \sin ω_{0}t [V_{A}e^{-1/T_{C}}] u(t)  V

= V_{A} [e^{-1/T_{C}} \sin ω_{0}t] u(t)  V

Figure 5–32 shows a graph of this waveform for T₀ = 2T_C. For t < 0 the step function forces the waveform to be zero. At t = 0, and periodically thereafter, the waveform passes through zero because sin(nπ) = 0. The waveform is not periodic, however, because the decaying exponential gradually reduces the amplitude of the oscillation. For all practical purposes the oscillations become negligibly small for t > 5T_C. The waveform obtained by multiplying a sinusoid by a decaying exponential is called a damped sine.