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k2 R

k2 R

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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k2 a Figure 1 2k, The mechanical system shown in Figure 1 consists of two springs attached to a pulley. The pulley has a radius R and a mass moment of inertia J while the springs have spring constants 2k; and k2. Assuming ideal springs and neglecting the effect of gravity on the pulley. „Assuming kj=11 N/m, k2=8 N/m, a=5 m, J=38 kg.m?, and R=11 m First, draw the Free Body Diagram of the system and clearly label all forces acting in it. Second. derive the equations of motion of the system for small oscillations using Newton's second law in the :form Equation of Motion: b40 + b30 + b20 + b¡0 + bo . where 0 is the angle that represents .the pully rotation. Third, find the natural frequency of the system (w).
Transcribed Image Text:k2 a Figure 1 2k, The mechanical system shown in Figure 1 consists of two springs attached to a pulley. The pulley has a radius R and a mass moment of inertia J while the springs have spring constants 2k; and k2. Assuming ideal springs and neglecting the effect of gravity on the pulley. „Assuming kj=11 N/m, k2=8 N/m, a=5 m, J=38 kg.m?, and R=11 m First, draw the Free Body Diagram of the system and clearly label all forces acting in it. Second. derive the equations of motion of the system for small oscillations using Newton's second law in the :form Equation of Motion: b40 + b30 + b20 + b¡0 + bo . where 0 is the angle that represents .the pully rotation. Third, find the natural frequency of the system (w).
:form Equation of Motlon: b40 + b30 +b½0 + b¡0 + bo , where 0 is the angle that represents .the pully rotation. Ihird. find the natural frequency of the system (w). „Finally, fill in the following blanks by the values of bi, and the natural freguency of the system (w)n Notes: 1) The coefficient of the higher part of the equation should be 1 Ex for third degree system: 6 + 46 + 20 + 50 + 3, Ex for secod degree system: 0 + 20 + 50 + 3, Ex for first degree system: 0 + 50 +3 1) You should fill the blanks with numbers only and with one decimal at max as EX: 12.1 2) The error is not cumulative and if you don't know any answer, just fill it with any random number more than 1 (zero is not acceptable). 1) The value of b,= 2) The value of b3 = 3) The value of b2 =
Transcribed Image Text::form Equation of Motlon: b40 + b30 +b½0 + b¡0 + bo , where 0 is the angle that represents .the pully rotation. Ihird. find the natural frequency of the system (w). „Finally, fill in the following blanks by the values of bi, and the natural freguency of the system (w)n Notes: 1) The coefficient of the higher part of the equation should be 1 Ex for third degree system: 6 + 46 + 20 + 50 + 3, Ex for secod degree system: 0 + 20 + 50 + 3, Ex for first degree system: 0 + 50 +3 1) You should fill the blanks with numbers only and with one decimal at max as EX: 12.1 2) The error is not cumulative and if you don't know any answer, just fill it with any random number more than 1 (zero is not acceptable). 1) The value of b,= 2) The value of b3 = 3) The value of b2 =
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