Consider the pendulum shown in Figure 1, where a small ball of mass m - 1kg suspended by a massless rod with length ofr=0.5m. Since the ball moves through air, air resistance will be experienced in a direction that is opposite to its velocity . Mathematically, we model the force as: 7 =-Bv² (1) 101 where B is a coefficient that depends on the shape of the ball and the density of the fluid (or air) in which it moves. Figure 1: Pendulum sketch. (a) Draw the free body diagram of the ball using polar coordinates (r - 8 in Figure), show the equation that describe the motion of 8 is given by: ö +²sine + sgn(8)8²r = 0 (2) where "sgn" is sign function that shows the sign of a real number, the definition is given by: (1 if x > 0 (3) sgn(x) =0 -1 if x = 0 if x < 0 (b) Convert the nonlinear differential equations obtained above for to states equations (see the appendix for details). Fill in the blanks in the provided main mix MATLAB code to generate the trajectory of 0,6 over time, with the help of ode45 solver in MATLAB.
Consider the pendulum shown in Figure 1, where a small ball of mass m - 1kg suspended by a massless rod with length ofr=0.5m. Since the ball moves through air, air resistance will be experienced in a direction that is opposite to its velocity . Mathematically, we model the force as: 7 =-Bv² (1) 101 where B is a coefficient that depends on the shape of the ball and the density of the fluid (or air) in which it moves. Figure 1: Pendulum sketch. (a) Draw the free body diagram of the ball using polar coordinates (r - 8 in Figure), show the equation that describe the motion of 8 is given by: ö +²sine + sgn(8)8²r = 0 (2) where "sgn" is sign function that shows the sign of a real number, the definition is given by: (1 if x > 0 (3) sgn(x) =0 -1 if x = 0 if x < 0 (b) Convert the nonlinear differential equations obtained above for to states equations (see the appendix for details). Fill in the blanks in the provided main mix MATLAB code to generate the trajectory of 0,6 over time, with the help of ode45 solver in MATLAB.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Please help me doing part B all I need help with is too make the derivation of equations of motion, and derivation of the state equations, and that will do for part B if you could help me with this it would make my life alot easier, and no matlab is not necessary for this.
Transcribed Image Text:Consider the pendulum shown in Figure 1, where a small ball of mass m=1kg suspended by a
massless rod with length of r=0.5m. Since the ball moves through air, air resistance will be
experienced in a direction that is opposite to its velocity. Mathematically, we model the force as:
7 =-Bv²/
(1)
where B is a coefficient that depends on the shape of the ball and the density of the fluid (or air)
in which it moves.
W
m
Figure 1: Pendulum sketch
(a) Draw the free body diagram of the ball using polar coordinates (r - 0 in Figure), show the
equation that describe the motion of is given by:
6 + sin0 +²sgn(0)8²r = 0
(2)
where "sgn" is sign function that shows the sign of a real number, the definition is given by:
(1
if x > 0
sgn(x)=0
(3)
-1
if x = 0
if x < 0
(b) Convert the nonlinear differential equations obtained above for to states equations (see the
appendix for details). Fill in the blanks in the provided main mix MATLAB code to generate
the trajectory of 0,6 over time, with the help of ode45 solver in MATLAB.
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