Still need help with Part d. ic+CVo-ilIoiRR+v A 10 mH inductor, a 1 uF capacitor, and a variable resistor are connected in parallelin the circuit shown. The resistor is adjusted so that the roots of the characteristicequation are -8000 j6000 rad/s. The initial voltage on the capacitor is 10 V, andthe initial current in the inductor is 80 mA. Finda. R;b. dv (0¹) /dt;c. B₁ and B₂ in the solution for v; andd. it (t).

Answered: d. i₁ (t).

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Still need help with Part d.

A 10 mH inductor, a 1 uF capacitor, and a variable resistor are connected in parallel
in the circuit shown. The resistor is adjusted so that the roots of the characteristic
equation are -8000 j6000 rad/s. The initial voltage on the capacitor is 10 V, and
the initial current in the inductor is 80 mA. Find
a. R;
b. dv (0¹) /dt;
c. B₁ and B₂ in the solution for v; and
d. it (t).

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I dont understand what is written for this answer. It is all jumbled together and hard to follow. Can somebody write it out so I can follow the steps better.

Given values for part C are: B1 = 10 V, B2 = -80/30V

The answer for part d is:

10e^8000t[8 cos 6000t + (82/3) sin 6000t] mA

But I dont understand the steps to arrive at this solution. Please help.

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