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Using the following o.d.e

[tex]

L\frac{d^2i}{dt^2}+R\frac{di}{dt}+\frac{1}{C}i=\frac{d}{dt}E(t)

[/tex]

The following problem has several parts all of which I have solved except for the one below.

L=1/20

R=5

[tex]

C=4.10^{-4}

[/tex]

[tex]

\frac{dE}{dt}=200\cos100t

[/tex]

Where L is an inductance in henries, R is a resistance in ohms, C is a capacitance in farads and E is the emf in volts.

The part I cannot agree with the book is as follows.

Firstly:

What should the frequency of the input E(t) be in order that it be in resonance with the system? [This I have solved correctly as :

[tex]

100\sqrt5

[/tex]

radians/sec

But this part leads to the next which I can't agree.

What is the maximum value of the current amplitude for this resonant frequency?

Book Answer= 2/5 amp.

John

[tex]

L\frac{d^2i}{dt^2}+R\frac{di}{dt}+\frac{1}{C}i=\frac{d}{dt}E(t)

[/tex]

The following problem has several parts all of which I have solved except for the one below.

L=1/20

R=5

[tex]

C=4.10^{-4}

[/tex]

[tex]

\frac{dE}{dt}=200\cos100t

[/tex]

Where L is an inductance in henries, R is a resistance in ohms, C is a capacitance in farads and E is the emf in volts.

The part I cannot agree with the book is as follows.

Firstly:

What should the frequency of the input E(t) be in order that it be in resonance with the system? [This I have solved correctly as :

[tex]

100\sqrt5

[/tex]

radians/sec

But this part leads to the next which I can't agree.

What is the maximum value of the current amplitude for this resonant frequency?

Book Answer= 2/5 amp.

John

Last edited: