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Problem 3 (10 points). Consider the weakly coupled mechanical system shown in figure 2. Let are:...
(3) (20 points) The (dimensionless) equations of motion for a frictionless double pendulum system...
please use mathematica for code NOT MATLAB
(3) (20 points) The (dimensionless) equations of motion for a frictionless double pendulum system as shown below (in the figure on the left) with mi m2 and L1 L are The solutions are graphed below (on the right) for the initial conditions θι (0) 2, θ1(0) 1.02(0) 0, and 02(0)-0 for oS t s 50. (a) Reformulate the IVP as a first order system.2 (b) Generate approximate solutions using any method (Euler, improved...
Mechanical vibration subject 3. a. Consider the system of Figure 3. If C1 = C2 =...
Mechanical vibration subject
3. a. Consider the system of Figure 3. If C1 = C2 = C3 = 0, develops the equation of motion and predict the mass and stiffness matrices. Note that setting k3 = 0 in your solution should result in the stiffness matrix given by [ky + kz -k2 kz b. constructs the characteristics equation from Question 3(a) for the case m1 = 9 kg, m2 = 1 kg, k1 = 24 N/m, k2 = 3 N/m,...
Problem 3: The system in Figure 3 consists of a double pendulum where both masses are...
Problem 3: The system in Figure 3 consists of a double pendulum where both masses are m and both lengths are L 2 Figure 3: System for Problem 3 (a) Derive the differential equations of motion for the system. The angles a(t) and θ2(t) can be arbitrarily large. (b) Linearize the equations by assuming that a (t) and 02(t) are small. Write the linearized differential equations in matrix form (c) Obtain the natural frequencies and modes of vibration. (d) Plot...
Question 3 (35 marks) Consider a mechanical system shown in Figure 3. The system is at rest for t
Question 3 (35 marks) Consider a mechanical system shown in Figure 3. The system is at rest for t<0. The input force f is applied at 0. The displacement x is the output of the system and is measured from the equilibrium position. kI b2 bi it Figure 3. Schematic of a mechanical system. (a) Obtain the traf) (10 marks) X (s) F(s) (b) Use of force-voltage analogy, obtain the equations for an electrical system (5 marks) (c) Draw a...
Question 3) Consider the mechanical system shown in figure, T(t) is the torque applied to shaft...
Question 3) Consider the mechanical system shown in figure, T(t) is the torque applied to shaft 1 and z(t) is the rotation of shaft 2. J.Jz and Jz are the inertias of shafts 1,2 and 3 respectively, N,,N,N, and N, are the number of teeths of the gears,, D1, D, and D3 are the coefficient of viscous damping associated with shafts 1, 2 and 3 respectively, K is the spring constant of the torsional spring attached to shaft 3. Write...
Consider the mechanical dynamics of a 2DOF rotary motion system shown below, where the torque is...
Consider the mechanical dynamics of a 2DOF rotary motion system shown below, where the torque is applied to the right shaft but the angular position of the left shaft is to be controlled, k is the stiffness of the linear rotary spring and bi, b2 are the viscous friction coefficients of the ball bearings that support the left and right shafts respectively and act as linear viscous dampers with rotary motion. PLEASE show all mathematical steps explicitly. (I1=Iz=1kgm², bi=b2=0.9Nms/rad, k=4Nm/rad)...
Question 1 Figure Q1 shows a mechanical system. The system input is T) and output is supposed to ...
Please write down the steps by steps solution, thank
you!
Question 1 Figure Q1 shows a mechanical system. The system input is T) and output is supposed to be 0. Please find the transfer function from T to θ 3, and discuss the stability of the system if the input is a unit impulse signal. (30 marks) To 01(t) 01t) I kg-m2 N 10 030) N2 100 100 kg-m2 100 N-m/rad 100 N-m-s/rad Figure Q1
Question 1 Figure Q1 shows...
Eigenproblerm. 4.34. Consider the system shown in Figure P4.28. Let k63 = 0, Determine the equati...
eigenproblerm. 4.34. Consider the system shown in Figure P4.28. Let k63 = 0, Determine the equations of motion. The rotational inertias are /1 and /2 and the angular stiffnesses equal ke, and ke, as in Figure P4.34. What are the system natural frequencies? ke, 4000 N-m, ker 6000 N-m, l- 1 kg m2, 12 2 kg-m θ3 02 12 Figure P4.28 ko θ2 Figure P4.34
eigenproblerm. 4.34. Consider the system shown in Figure P4.28. Let k63 = 0, Determine the...
θ2(s)/T(s) for the following rotational mechanical system Problem 4: Find the transfer function G(s) TO) N1...
θ2(s)/T(s) for the following rotational mechanical system Problem 4: Find the transfer function G(s) TO) N1 = 4 Di 1 N-m-s/rad N2 121 kg-m2 N3-4 D2-2 N-m-s/rad K 64 N-m/rad- N4 16 D3 32 N-m-s/rad -16 kg-m2 000
Problem-5 (20 pts): Consider the DC servo motor shown in Figure-5. Assume that the input of the s...
Problem-5 (20 pts): Consider the DC servo motor shown in Figure-5. Assume that the input of the system is the applied armature voltage ea and the output is the load shaft position θ2. Assume also the following numerical values for the components: Ra-) Armature winding resistance = 0.2Ω La → Armature winding inductance = 0.1 mH Kb-) Back emf constant 0.05 Vs/rad K > Motor torque constant 0.06 Nm/A Jr Moment of inertia of the rotor of the motor =...
please use mathematica for code NOT MATLAB
(3) (20 points) The (dimensionless) equations of motion for a frictionless double pendulum system as shown below (in the figure on the left) with mi m2 and L1 L are The solutions are graphed below (on the right) for the initial conditions θι (0) 2, θ1(0) 1.02(0) 0, and 02(0)-0 for oS t s 50. (a) Reformulate the IVP as a first order system.2 (b) Generate approximate solutions using any method (Euler, improved...
Mechanical vibration subject
3. a. Consider the system of Figure 3. If C1 = C2 = C3 = 0, develops the equation of motion and predict the mass and stiffness matrices. Note that setting k3 = 0 in your solution should result in the stiffness matrix given by [ky + kz -k2 kz b. constructs the characteristics equation from Question 3(a) for the case m1 = 9 kg, m2 = 1 kg, k1 = 24 N/m, k2 = 3 N/m,...
Problem 3: The system in Figure 3 consists of a double pendulum where both masses are m and both lengths are L 2 Figure 3: System for Problem 3 (a) Derive the differential equations of motion for the system. The angles a(t) and θ2(t) can be arbitrarily large. (b) Linearize the equations by assuming that a (t) and 02(t) are small. Write the linearized differential equations in matrix form (c) Obtain the natural frequencies and modes of vibration. (d) Plot...
Question 3 (35 marks) Consider a mechanical system shown in Figure 3. The system is at rest for t<0. The input force f is applied at 0. The displacement x is the output of the system and is measured from the equilibrium position. kI b2 bi it Figure 3. Schematic of a mechanical system. (a) Obtain the traf) (10 marks) X (s) F(s) (b) Use of force-voltage analogy, obtain the equations for an electrical system (5 marks) (c) Draw a...
Question 3) Consider the mechanical system shown in figure, T(t) is the torque applied to shaft 1 and z(t) is the rotation of shaft 2. J.Jz and Jz are the inertias of shafts 1,2 and 3 respectively, N,,N,N, and N, are the number of teeths of the gears,, D1, D, and D3 are the coefficient of viscous damping associated with shafts 1, 2 and 3 respectively, K is the spring constant of the torsional spring attached to shaft 3. Write...
Consider the mechanical dynamics of a 2DOF rotary motion system shown below, where the torque is applied to the right shaft but the angular position of the left shaft is to be controlled, k is the stiffness of the linear rotary spring and bi, b2 are the viscous friction coefficients of the ball bearings that support the left and right shafts respectively and act as linear viscous dampers with rotary motion. PLEASE show all mathematical steps explicitly. (I1=Iz=1kgm², bi=b2=0.9Nms/rad, k=4Nm/rad)...
Please write down the steps by steps solution, thank
you!
Question 1 Figure Q1 shows a mechanical system. The system input is T) and output is supposed to be 0. Please find the transfer function from T to θ 3, and discuss the stability of the system if the input is a unit impulse signal. (30 marks) To 01(t) 01t) I kg-m2 N 10 030) N2 100 100 kg-m2 100 N-m/rad 100 N-m-s/rad Figure Q1
Question 1 Figure Q1 shows...
eigenproblerm. 4.34. Consider the system shown in Figure P4.28. Let k63 = 0, Determine the equations of motion. The rotational inertias are /1 and /2 and the angular stiffnesses equal ke, and ke, as in Figure P4.34. What are the system natural frequencies? ke, 4000 N-m, ker 6000 N-m, l- 1 kg m2, 12 2 kg-m θ3 02 12 Figure P4.28 ko θ2 Figure P4.34
eigenproblerm. 4.34. Consider the system shown in Figure P4.28. Let k63 = 0, Determine the...
θ2(s)/T(s) for the following rotational mechanical system Problem 4: Find the transfer function G(s) TO) N1 = 4 Di 1 N-m-s/rad N2 121 kg-m2 N3-4 D2-2 N-m-s/rad K 64 N-m/rad- N4 16 D3 32 N-m-s/rad -16 kg-m2 000
Problem-5 (20 pts): Consider the DC servo motor shown in Figure-5. Assume that the input of the system is the applied armature voltage ea and the output is the load shaft position θ2. Assume also the following numerical values for the components: Ra-) Armature winding resistance = 0.2Ω La → Armature winding inductance = 0.1 mH Kb-) Back emf constant 0.05 Vs/rad K > Motor torque constant 0.06 Nm/A Jr Moment of inertia of the rotor of the motor =...
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