Final answer:
The student is asked to model an RLC circuit with a differential equation and solve for the charge q(t) given specific initial conditions. The correct differential equation is Lq''(t) + Rq'(t) + (1/C)q(t) = E(t), where E(t) = 0 for a constant voltage. To solve for q(t), one would typically find the roots of the characteristic equation and apply the initial conditions.
Step-by-step explanation:
RLC Circuit Differential Equation
The question is asking to write down the differential equation modeling the charge in an LRC loop series circuit (which is equivalent to an RLC circuit) with the given values of L, R, and C, and then solve it given an initial voltage and initial conditions for charge q(0) and its derivative q'(0). The differential equation for an RLC series circuit is derived from Kirchhoff's voltage law, which in this case can be written as:
Lq''(t) + Rq'(t) + \(\frac{1}{C}\)q(t) = E(t)
Given that the impressed voltage E is constant and equal to zero (E(t) = 0), and considering the given initial conditions q(0) = 2 and q'(0) = 5, the particular solution for the charge q(t) can be found by solving the homogeneous second-order linear differential equation:
Lq''(t) + Rq'(t) + \(\frac{1}{C}\)q(t) = 0
The solution typically involves finding the characteristic equation, solving for the roots, and then applying the initial conditions to determine the constants for the particular solution of q(t).
However, it is important to note that in this question, there seems to be a typo in the values provided. To compute the correct answer, we would need the correct values of L, R, and C.