Mathematical Modeling & Simulation
Home Work # 3
Due date: 8 days after the distribution.
1. Employing MATLAB-Simulink, perform a simulation of y versus time
t = 0.1 and
9.00 t
. Employ a
method of your choice and compare it with the exact solution:
2
ty
dt
dy
, where y(0) = 1.0
Vary the step size and observe the effect on accuracy. Plot results.
2. Solve a simple second order differential equation on Simulink:
Adt/xd
22
for various choices of A. Plot results on one graph.
Use x(0) = 0.0, dx/dt = 1.0 at t=0. Then Plot the x(t) versus time on
a graph and then also plot on separate graph dx/dt versus x(t) on
a graph for various values of initial conditions.
3. A mass (m = 1kg) is falling under gravity from height h = 500 m. At
y = 100 m, velocity = 0 at time t = 0. and y(0) = 100. Consider that
the acceleration due to gravity g is function of y (altitude) and a
drag force is proportional to the square of the velocity (with
proportionality constant equal to 1.0). After develop the equation-
based model of the system, simulate it using MATLAB-Simulink.
Plot results.
4. What do you understand by symbolic computing? What is meant
by an analytical solution of ODE by MATLAB? Try solving a simple
nonlinear second order differential equation:
tsinAdt/xd
22
using MATLAB-simulink. Use x(0) = 0.0, dx/dt = 1.0 at t=0.
Choose different time steps and values of A.
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