Question: The following ODE models the motion of a damped pendulum with forcing. y (t) + 5y' (t) + 6y(t) = 3 cost, y(0) =

The following ODE models the motion of a damped pendulum with forcing.

The following ODE models the motion of a damped pendulum with forcing. y" (t) + 5y' (t) + 6y(t) = 3 cost, y(0) = 1, y'(0) = 0. 2.1. Find the exact analytical solution y(t) (you may plot results over 0 < t 2). 2.2. Implement a finite difference scheme of your choice, and discuss its accuracy. Marks are given for deriving the recurrence formula and the recurrence seeds. 2.3. Illustrate the convergence and the order of accuracy for your chosen scheme, by plotting the results against the exact solution for different values of the time step. 2.4. Formulate a second order accurate method throughout (recurrence and seeds).

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