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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Answer to a math 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
Eliseo
4.690 Answers
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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