Question: Design a parallel (R L C) circuit whose natural response has the form [ v_{mathrm{L}}(t)=K_{1} e^{-20,000 t}+K_{2} t e^{-20,000 t} mathrm{~V} quad t geq 0

Design a parallel $R L C$ circuit whose natural response has the form

\[
v_{\mathrm{L}}(t)=K_{1} e^{-20,000 t}+K_{2} t e^{-20,000 t} \mathrm{~V} \quad t \geq 0
\]

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