Pertemuan VIII
Aplikasi
Second Order Linear DEs
Example
In a series RCL circuit driven by a constant emf, the natural
response of the circuit is given by
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for which the initial conditions are i(0)=0 A and
at t=0 is 4.
State the nature of response of the current and hence solve for i.
Solution:
We will solve this in the same way as the previous section.
A.E.
, Solution is:
The response is critically damped, since the roots are equal.
So we can now write:
Therefore
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Second Order Linear DEs
In a RCL series circuit,
,
voltage source is
given that at time
F,
V. Solve for the current
H and the
in the circuit
, the current in the circuit is zero and the
charge in the capacitor is
C.
Differentiating gives a 2nd order DE in :
A.E:
, Solution is:
So
So
We need to find the value of
At
.
,
Now returning to equation (1):
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Now, at time
,
So
So
Therefore,
SN Solution:
We need to set it up in terms of only, to give us a DE which SN can
solve:
To get , we simply differentiate:
a. Natural Response
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b. Forced Response
Let us now have as our EMF
Natural:
Forced:
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Terima kasih
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