Part c - numerical methods (10 marks) charlie the cyclist (from portfolio 2) would now like to analyse an ode of his velocity while pedalling on his bicycle. this will lead to a non-linear, non- separabe ode, so he would like for the velocity to be solved numerically. for any forcing function, his bike can be described with the ode du d2_f(t) + - 0 dt ' m m charlie approximates that his pedalling results in a forcing function of f(t) = 100 + 100 sin(8t) n. he has a mass of m= 70 kg, his drag coefficient is d=1 kg/m and his initial velocity is v(0) = 0. 1. use matlab's ode45 function to approximate charlie's velocity while riding his bike. plot your solution from t=0s tot = 30 s using matlab. (2 mark) 2. use the euler function on blackboard to approximate charlie's velocity using h=2. plot the solution in the same figure as your ode45 solution, and comment on the accuracy of the euler solution. (2 marks) 3. recommend to charlie what step size should be used in euler's method in order to obtain a sufficiently accurate solution for velocity without wast- ing computational time. in your solution, clearly state how you defined "sufficiently accurate" and provide reasoning for your decision (including any relevant code, plots and/or metrics). (3 marks) 4. charlie is interested in modelling both his velocity and position while rid- ing his bike. create a system of odes with velocity and position as the two dependant variables, and use matlab's ode45 function to solve (as- sume initial position is 0). plot the position from t=0 s to t= 30 s using matlab (3 marks)