Homework Answers
1. (a) It is a non linear system, so the state space representation will not be in the form of the state space matrices for linear form. We can write,
Substituting we can write the equations as,
In complete matrix form we can write,
This is the state space representation of a non linear system.
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Mathematical model: A simple mathematical model that describes the equations of motion is given as: m...
CODE GIVEN % Create a program to plot the motion of the ping pong ball with...
CODE GIVEN
% Create a program to plot the motion of the ping pong ball with
drag.
% The program will take inputs for velocity in m/s and angle of
launch.
% note that with a high speed camera I estmated a launch speed
for a ping
% pong ball could be 30 m/s.
vel=30; %m/s
angle=60;
% convert the degrees into radians so MATLAB likes it
angle=angle*pi/180;
% set initial values (time, distance, mass, gravity, drag)
x(1)=0; % meters...
A particle P of mass m kg is attached to two fixed points A and B by two identical model springs,...
A particle P of mass m kg is attached to two fixed points A and B by two identical model springs, each of stiffness k and natural length lo- The point A is at a height 1/o above the point B. The particle is free to oscillate vertically under gravity. The stiffness of each spring is given by k = 4mg/10. The horizontal level passing through the fixed point A is taken as the datum for the gravitational potential energy....
Use Matlab... Use given variables... %Set values of parameters H0 = 4000 ; v0 = 0; vplane = 38.9...
Use Matlab... Use given variables...
%Set values of parameters
H0 = 4000 ;
v0 = 0;
vplane = 38.9;
vwind = 7.0;
g = -9.81;
td = 45;
dt = 0.1;
%initial conditions
%To minimize edits, let v = vertical velocity, and vx = horizontal
velocity
y(1) = H0;
v(1) = v0;
t(1) = 0;
x(1) = 0;
vx(1) = vplane;
%loop until parachutist reaches the ground
%Calculate te horizontal distance traveled before and after the
parachute opens
d_free =...
1. A football has a mass of mp = 0.413 kg. It can be approximated as...
1. A football has a mass of mp = 0.413 kg. It can be approximated as an ellipsoid 6 in diameter and 12 in long. A 'Hail Mary' pass is thrown upward at a 45° angle with an initial velocity of 55 mph. Air density at sea level is p= 1.22 kg/m². Neglect any spin on the ball and any lift force. Assume turbulent flow and a constant air-drag coefficient of Cp = 0.13. The equation of motion of the...
Need help solving these two second order differential equations, the picture below are the answers to...
Need help solving these two second order differential
equations, the picture below are the answers to them. I'm just
stuck on how to work them out to get those solutions
3 Assignments 3.1 Analysis in the absence of air resistance Ignoring alr resistance, Newton's equations of motion for an object under the influence of gravity alone are quite straightforward. We're also ignoring the fact that the gravitational pull on an object above the earth depends upon its height above the...
CODE GIVEN
% Create a program to plot the motion of the ping pong ball with
drag.
% The program will take inputs for velocity in m/s and angle of
launch.
% note that with a high speed camera I estmated a launch speed
for a ping
% pong ball could be 30 m/s.
vel=30; %m/s
angle=60;
% convert the degrees into radians so MATLAB likes it
angle=angle*pi/180;
% set initial values (time, distance, mass, gravity, drag)
x(1)=0; % meters...
A particle P of mass m kg is attached to two fixed points A and B by two identical model springs, each of stiffness k and natural length lo- The point A is at a height 1/o above the point B. The particle is free to oscillate vertically under gravity. The stiffness of each spring is given by k = 4mg/10. The horizontal level passing through the fixed point A is taken as the datum for the gravitational potential energy....
Use Matlab... Use given variables...
%Set values of parameters
H0 = 4000 ;
v0 = 0;
vplane = 38.9;
vwind = 7.0;
g = -9.81;
td = 45;
dt = 0.1;
%initial conditions
%To minimize edits, let v = vertical velocity, and vx = horizontal
velocity
y(1) = H0;
v(1) = v0;
t(1) = 0;
x(1) = 0;
vx(1) = vplane;
%loop until parachutist reaches the ground
%Calculate te horizontal distance traveled before and after the
parachute opens
d_free =...
1. A football has a mass of mp = 0.413 kg. It can be approximated as an ellipsoid 6 in diameter and 12 in long. A 'Hail Mary' pass is thrown upward at a 45° angle with an initial velocity of 55 mph. Air density at sea level is p= 1.22 kg/m². Neglect any spin on the ball and any lift force. Assume turbulent flow and a constant air-drag coefficient of Cp = 0.13. The equation of motion of the...
Need help solving these two second order differential
equations, the picture below are the answers to them. I'm just
stuck on how to work them out to get those solutions
3 Assignments 3.1 Analysis in the absence of air resistance Ignoring alr resistance, Newton's equations of motion for an object under the influence of gravity alone are quite straightforward. We're also ignoring the fact that the gravitational pull on an object above the earth depends upon its height above the...
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