Please forgive my lack of recall with respect to DE's. It's been a few years.
For parts b and c I understand that we take the derivative and set it equal to zero to find a max but I'm not sure what we solve for at that point. I assume it's t. I think that would give us the time at which v is at max. Am I correct in this approach?
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Are you talking about Problem 2 or Problem 1?
In Prob 1, you need to manipulate your v' function into something you can plug into a trig identity to get rid of the cosine term. Same with i'. Once you get it in terms of sin(something-something else) it will become abundantly clear.
y(t) = Acos(wnt) + B sin(wnt) + Constant.......this can be transformed into z(t) = Dsin(wnt + phi)+ Constant........D = sqrt(A^2 + B^2)....which is the amplitude. The constant is an offset that shifts the function up or down.
There is an easier way to solve part d and e, without taking any derivatives:
part d:
v(at the time when i=max)=?
i=max when di/dt=0;
v(L)=L*di/dt=0 volts at the time when i=max. Voltage on the inductor is zero at the time when i=max. From the circuit (fig1-pb1) what is v(C) at the time when i=max, if voltage on the inductor is zero?
part e:
i(at the time when v=max)=?
v=max when dv/dt=0;
i(C)=C*dv/dt=0 volts at the time when v=max. Capacitor current is zero at the time when v=max. From the circuit (fig1-pb1) what is i(L) at the time when v=max, if capacitor current is zero?
correction on part e:
i(C)=C*dv/dt=0 amps not volts
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