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The current I(t) in an LC series circuit is governed by the initial value problem below Determine the current as function of time72 sin t 0stszr 1"(4)+ 251(t) ...

Question

The current I(t) in an LC series circuit is governed by the initial value problem below Determine the current as function of time72 sin t 0stszr 1"(4)+ 251(t) = g(t) , I(0) = 2,1'(0) = 18, where g(t) = 2r<tClick here _to_view the_table_of Laplace transforms Click here_to_view the_table ofproperties of Laplace transfomsI(t) =

The current I(t) in an LC series circuit is governed by the initial value problem below Determine the current as function of time 72 sin t 0stszr 1"(4)+ 251(t) = g(t) , I(0) = 2,1'(0) = 18, where g(t) = 2r<t Click here _to_view the_table_of Laplace transforms Click here_to_view the_table ofproperties of Laplace transfoms I(t) =



Answers

The current $I(t)$ in an $L C$ series circuit is governed by the initial value problem $$I^{\prime \prime}(t)+4 I(t)=g(t)$$
$$I(0)=1, \quad I^{\prime}(0)=3$$
where
$$g(t) : \left\{\begin{array}{ll}{3 \sin t,} & {0 \leq t \leq 2 \pi} \\ {0,} & {2 \pi< t}\end{array}\right.$$
Determine the current as a function of time $t .$

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