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The current, I, in an RLC circuit is given by the equation: R d’I dI + 2a +®;I = 0 (1) dt? dt V C where the damping factor, a, and resonant frequency, w, =Vo² +a² , are dependent on the values of the resistor, R, capacitor, C, and inductor L: 1 R and @. 2L a = VLC A solution of equation (1) is given by I(t) = e -at sin ot (2) (a) Determine the first and second derivatives of I(t) and hence show that /(t) is a solution of equation (1). (b) Show that the stationary points of I(t) =e -at sin ot occur at time t: tan ot = (c) Determine the partial derivatives ôw, ôw.

The current, I, in an RLC circuit is given by the equation: R d’I dI + 2a +®;I = 0 (1) dt? dt V C where the damping factor, a, and resonant frequency, w, =Vo² +a² , are dependent on the values of the resistor, R, capacitor, C, and inductor L: 1 R and @. 2L a = VLC A solution of equation (1) is given by I(t) = e -at sin ot (2) (a) Determine the first and second derivatives of I(t) and hence show that /(t) is a solution of equation (1). (b) Show that the stationary points of I(t) =e -at sin ot occur at time t: tan ot = (c) Determine the partial derivatives ôw, ôw.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi, can you help me with all parts of this question, parts a,b,and c?

thank you

Question 1 The current, I, in an RLC circuit is given by the equation: R d²I dI + 2a + wI = 0 (1) dt? dt where the damping factor, a, and resonant frequency, o, = Vo? +a? , are dependent on the values of the resistor, R, capacitor, C, and inductor L: 1 R and @o 2L a = VIC A solution of equation (1) is given by -at I(t) = e-" sin ot (2) (a) Determine the first and second derivatives of /(t) and hence show that /(t) is a solution of equation (1). (b) Show that the stationary points of I(t) = e" sin wt occur at time t: tan ot = (c) Determine the partial derivatives De , Te
Transcribed Image Text:Question 1 The current, I, in an RLC circuit is given by the equation: R d²I dI + 2a + wI = 0 (1) dt? dt where the damping factor, a, and resonant frequency, o, = Vo? +a? , are dependent on the values of the resistor, R, capacitor, C, and inductor L: 1 R and @o 2L a = VIC A solution of equation (1) is given by -at I(t) = e-" sin ot (2) (a) Determine the first and second derivatives of /(t) and hence show that /(t) is a solution of equation (1). (b) Show that the stationary points of I(t) = e" sin wt occur at time t: tan ot = (c) Determine the partial derivatives De , Te
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