advertisement

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: VIII-1 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 VIII-2 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 , VIII-3 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 VIII-4 b. Forced Response Let us now have as our EMF Natural: Forced: VIII-5 VIII-6 VIII-7 VIII-8 VIII-9 TERIMA KASIH VIII-10