Question

Find a function of (t) an instantaneous frequency of a voltage waveform function v(t) = 10 cos{2π)[(100kt + sin(300πt)}

Answer 1

The instantaneous frequency (f) of the voltage waveform function
`\( v(t) = 10 \cos[2\pi(100kt + \sin(300\pi t))] \)` is given by
`\( f(t) = 100k - 300 \cos(300\pi t) \).`

Step-by-step explanation:

To find the instantaneous frequency of the given voltage waveform function
`\( v(t) \),` we start by identifying the argument inside the cosine function. The argument is
`\( 2\pi(100kt + \sin(300\pi t)) \).` The instantaneous frequency is the derivative of this argument with respect to time (t). Therefore,
`\( f(t) = (d)/(dt)[2\pi(100kt + \sin(300\pi t))] \).` The derivative involves finding the rate of change with respect to time, resulting in
`\( f(t) = 100k - 300 \cos(300\pi t) \).`

The instantaneous frequency function
`\( f(t) \)` reflects how the frequency of the voltage waveform changes at each moment in time. The term
`\( 100k \)` represents the constant frequency component, while the term
`\( -300 \cos(300\pi t) \)` accounts for the modulation introduced by the sinusoidal term
`\( \sin(300\pi t) \).` This modulation results in variations in the instantaneous frequency, providing a detailed understanding of how the frequency changes dynamically in the given voltage waveform.

The process of finding instantaneous frequency is a fundamental concept in signal processing and communication engineering. It allows us to analyze the frequency content of time-varying signals, providing insights into the behavior of complex waveforms. In this case, the obtained function
`\( f(t) \)` describes the instantaneous frequency of the voltage waveform
`\( v(t) \)` at any given time
`\( t \),` incorporating both constant and modulated frequency components.