An RLC circuit governed by the equation Lq” + Rq’ + q/C = E(t) has inductance L = 2 Henry, resistance R = 4 Ohms and capacitance C = 0.5 C (where q(t) is the charge at time t). Find an explicit expression for the current I(t) = q'(t) at every time t, if the voltage drop across the source is E = 0, and that the charge starts from q(0) = 1 and q'(0) = 0. AND same question if the capacitance is decreased to C = 0.25 and resistance is increased to R = 6.

An RLC circuit governed by the equation Lq” + Rq’ + q/C = E(t) has inductance
L = 2 Henry, resistance R = 4 Ohms and capacitance C = 0.5 C (where q(t) is the
charge at time t).

Find an explicit expression for the current I(t) = q'(t) at every time t, if
the voltage drop across the source is E = 0, and that the charge starts from
q(0) = 1 and q'(0) = 0.

AND same question if the capacitance is decreased to C = 0.25 and resistance
is increased to R = 6.5

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