Question

Apply the forcing function v(t) 60e−2t cos(4t + 10°) V to the RLC circuit in series of Figure 14.1 and specify the forced response by determining the values of Im and φ in the expression i(t) Ime−2t cos(4t + φ) in the domain of time

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Eliseo

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1. Given the forcing function:

v(t) = 60e^{-2t} \cos(4t + 10^\circ)

2. The expression for the forced response is:

i(t) = I_me^{-2t} \cos(4t + \phi)

3. By comparing the two expressions:

60e^{-2t} \cos(4t + 10^\circ) \quad \text{and} \quad I_me^{-2t} \cos(4t + \phi)

we can determine:

I_m = 60 \quad \text{and} \quad \phi = 10^\circ

4. Thus, the values are:

I_m = 60

\phi = 10^\circ

2. The expression for the forced response is:

3. By comparing the two expressions:

we can determine:

4. Thus, the values are:

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