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Consider the system shown in the figure below. Assume that when z is zero, that the spring is at its unstretched length. That is, the restoring force in the spring only develops when z, (the figure is a little misleading here). Note that z, is defined as positive to the left and zgis defined as positive downwards.

Consider the system shown in the figure below. Assume that when z is zero, that the spring is at its unstretched length. That is, the restoring force in the spring only develops when z, (the figure is a little misleading here). Note that z, is defined as positive to the left and zgis defined as positive downwards.

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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Consider the system shown in the figure below. Assume that when z is zero, that the spring is at its unstretched length. That is, the restoring force in the spring only develops when z, (the figure is a little misleading here). Note that z, is defined as positive to the left and zg is defined as positive downwards. Syntax notes: when entering your responses, use x[1] for z1and x2] for z2. m[1] for m1. m[2] for mg, and g for gravity. Use T for the tension in the rope. You can use the loupimagnifying glass to check that what you entered is what you intended. Kinematics The change in z is related to the change in zgsince they are part of the same string. What is the kinematic relationship between the two of them? 21- -2x(2] Kinetic Energy Write the total system kinetic energy. (ie write it in terms of both z1and zgand their velocities). Use diffio(1]t).) for ż and diffx(2]t).1) for ż KE = (12)m[1]*(difix[1]{t),f)^2+(1/2}*m[2]*(diff(x{2]{t),f)^2 Now use your kinematic relationship to write the system kinetic energy ONLY in terms of z2 KE = (1/2)(4*m[1]+m[2]}*(diff(x(2](t).t)*2 The equivalent system mass corresponding to the variable z2 is given by meq = 4*m[1]+m[2] Potential Energy The elastic potential energy of the system is given by (this means potential energy due to springs - ie elasticity). Here, write it in terms of its 'natural variable, which is z PE springe The elastic potential energy written in terms of z3 (use the kinematic relationship) is given by PE springs Section Attempt 1 of 5 Verify
Transcribed Image Text:Consider the system shown in the figure below. Assume that when z is zero, that the spring is at its unstretched length. That is, the restoring force in the spring only develops when z, (the figure is a little misleading here). Note that z, is defined as positive to the left and zg is defined as positive downwards. Syntax notes: when entering your responses, use x[1] for z1and x2] for z2. m[1] for m1. m[2] for mg, and g for gravity. Use T for the tension in the rope. You can use the loupimagnifying glass to check that what you entered is what you intended. Kinematics The change in z is related to the change in zgsince they are part of the same string. What is the kinematic relationship between the two of them? 21- -2x(2] Kinetic Energy Write the total system kinetic energy. (ie write it in terms of both z1and zgand their velocities). Use diffio(1]t).) for ż and diffx(2]t).1) for ż KE = (12)m[1]*(difix[1]{t),f)^2+(1/2}*m[2]*(diff(x{2]{t),f)^2 Now use your kinematic relationship to write the system kinetic energy ONLY in terms of z2 KE = (1/2)(4*m[1]+m[2]}*(diff(x(2](t).t)*2 The equivalent system mass corresponding to the variable z2 is given by meq = 4*m[1]+m[2] Potential Energy The elastic potential energy of the system is given by (this means potential energy due to springs - ie elasticity). Here, write it in terms of its 'natural variable, which is z PE springe The elastic potential energy written in terms of z3 (use the kinematic relationship) is given by PE springs Section Attempt 1 of 5 Verify
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