We Helped With This MATLAB Programming Homework: Have A Similar One?

ENME 303 HW12

Due Monday, December 10th by 10:00 am

For each problem, submit: a copy of any script and function used in the problem (m), a copy of the command line input/output associated with the problem, any plots generated, and a brief summary (one or two sentences).

Problem 1  

The rate of heat flow by conduction between two points on a cylinder heated at one end is given by

         ^{dQ         dT}             where                                     λ_A  == constant cylinder’s cross sectional area                              Tt ₌ = time temperature        

__A ^{dt  dx}                        Q = Heat flow      x = distance from the heated end

Because the equation involves two derivatives, we will simplify this equation by letting 

                        dT      100(L x)(20t)                        where     L = length of the rod



                        dx             100 xt

Combine the two equations and compute the heat flow for t = 0 to 25 s using the Euler’s method and the second order Runge-Kutta methods (Heun). The initial condition is Q(0) = 0 and the parameters are λ = 0.5 cal·cm/s, A = 12 cm², L = 20 cm and x = 2.5 cm. Plot your results in one graph and comment on your results.

Problem 2

The following equation can be used to model the deflection of a sailboat mast subject to a wind force:

                                                                             d y2              f              2

                                                                                             L z 

dz2 2EI

where f = wind force, E = modulus of elasticity, L = mast length, and I = moment of inertia. Note that the second order differential equation can be decoupled into the following two first order differential equations:

dy  w           dw _ f L_ z2 dz         dz 2EI

Write a program that uses the fourth-order Runge-Kutta method to calculate the deflection distribution along the mast and plot it against z if y = 0 and dy/dz = 0 at z = 0. Use parameter values of f = 60, L = 30, E = 1.25 × 10⁸, and I = 0.05 for your computation.