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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: ƒ=-Bv². 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. (1) 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: + sine+sgn(0)0²r = 0 (2) where "sgn" is sign function that shows the sign of a real number, the definition is given by: 1 sgn(x)=0 if x > 0 if x = 0 if x < 0 (3) (b) Convert the nonlinear differential equations obtained above for Ö to states equations (see the -1

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: ƒ=-Bv². 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. (1) 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: + sine+sgn(0)0²r = 0 (2) where "sgn" is sign function that shows the sign of a real number, the definition is given by: 1 sgn(x)=0 if x > 0 if x = 0 if x < 0 (3) (b) Convert the nonlinear differential equations obtained above for Ö to states equations (see the -1

Elements Of Electromagnetics
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 show all work!! Do A and B together please.

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 v. Mathematically, we model the force as: ƒ =-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. 9 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: + sin0 += sgn(0)8²r = 0 m (2) where "sgn" is sign function that shows the sign of a real number, the definition is given by: 1 sgn(x) = 0 if x > 0 if x = 0 if x < 0 (3) (b) Convert the nonlinear differential equations obtained above for Ö to states equations (see the -1
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 v. Mathematically, we model the force as: ƒ =-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. 9 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: + sin0 += sgn(0)8²r = 0 m (2) where "sgn" is sign function that shows the sign of a real number, the definition is given by: 1 sgn(x) = 0 if x > 0 if x = 0 if x < 0 (3) (b) Convert the nonlinear differential equations obtained above for Ö to states equations (see the -1
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