Consider the electronic circuit shown below. The charge of the capacitor obeys the following differential equation:
\[ \frac{d^2q}{dt^2} + p \frac{dq}{dt} + q = 0 \]
with initial conditions: \( q_0 = 0 \) and \( \frac{dq}{dt} \bigg|_{t=0} = 1.0 \)
2-a) Use the Laplace transformation method to find \( Q(p) \), which is just the Laplace transform of the solution \( q(t) \) of this equation?
2-b) Find the Laplace inverse of \( Q(p) \) to get the solution \( q(t) \).