1. A number of systems are specified below in terms of their input-output relationships. For each case, determine if the system is linear and/or time-invariant.
a.
b.
c.
d. λ)dλ
e.
f.
2. Find a differential equation between the input voltage x(t) and the output voltage y(t) for the circuit shown below. At t = 0 the initial values are
iL(0) = 1 A VC(0) = 2 V
Express the initial conditions for y(t) and dy(t)/dt
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3. Find a differential equation between the input voltage x(t) and the output voltage y(t) for the circuit below. At t=0 the initial values are
V1(0) = 2 V V2(0) = -2 V
Express the initial conditions for y(t) and dy(t)/dt
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4. Solve each of the first-order differential equations given below for the specified input signal and subject to the specified initial condition. Use the first-order solution technique
a.
b.
c.
d.
e.
5. For each homogeneous differential equation given below, find the characteristic equation and show that at least some of its roots are complex. Find the homogeneous solution for t ≥ 0 in each case subject to the initial conditions specified.
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