Please solve 7.99!!!! d^2 v_1 (t)/dt^2 + 2[dv_1(t)/dt] + 5v_1 (t) = 0 Find the c

Question

Please solve 7.99!!!!

d^2 v_1 (t)/dt^2 + 2[dv_1(t)/dt] + 5v_1 (t) = 0 Find the characteristic equation of the network. the circuit's natural frequencies. the expression for v_1(t). The output voltage of a circuit is described by the differential equation d^2 vb_0(t)/dt^2 + 8 dv_0(t)/dt + 10 v_0 (t) = 0 Find the characteristic equation of the circuit, the network's natural frequencies, and the equation for v_0(t). A parallel RLC circuit contains a resistor R = 1 Ohm and an inductor L = 2H. Select the value of the capacitor so that the circuit is critically damped.

Explanation / Answer

a) characteristic equation is m^2+8m+10=0

b) roots of characteristic equation are -1.55 and -6.45

if roots exist in the form a+ib form natural frequency is b here b=0 so natural frequency is zero

c) sollution of homogenious equation Vo(t) = x e^-1.55t + y e^-6.45t

here x and y are calculated by initial conditions

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