# PERTEMUAN X APPLIKASI Second Order Linear DEs ```PERTEMUAN X
APPLIKASI
Second Order Linear DEs
Example
In a series RCL circuit driven by a constant emf, the natural
response of the circuit is given by
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:
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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
Second Order Linear DEs
In a RCL series circuit,
voltage source is
,
F,
V. Solve for the current
H and the
in the circuit
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given that at time
, 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):
Now, at time
,
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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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