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For the system in the figure betow, find the differential equations that relate between the input...
3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the output function of the system. Assume gravity is not a factor. of...
3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the output function of the system. Assume gravity is not a factor. of the system, find the transfer f (t) C3 m2 mi Figure 1
3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the...
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or...
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
5. Figure 5 shows an electrical network, i) obtain the differential equations of the network and nofind the tran...
5. Figure 5 shows an electrical network, i) obtain the differential equations of the network and nofind the transfer function F(s) show that the same transfer function is obtained 12(s)/Vin(s); ii) Analyse the circuit in the s-domain and R. C i2(t) Vin(t) L Figure 5. Electrical Network 4. Find the transfer function X2(s)/F(s) of the spring-mass system shown in Figure 4. The system moves over a frictionless surface. h M2 M1 Figure 4. A 2 DOF spring-mass system over a...
Q2. A mechanical system is shown as Figure 2, where external force uz is the input...
Q2. A mechanical system is shown as Figure 2, where external force uz is the input and displacement y2 is the output. The force acting on m2 has a linear relationship with uj as u2=Aui. 1) List system equations; 2) Draw block diagram of the control system; 3) Build the block diagram in Simulink (screenshot and paste your diagram in your submission). ki U1 mi k2 Yi Y bi U2 V m2 y2 Figure 2
A Mechanical system is shown in Fig. 1.1. a) Obtain a set of simultaneous integro-differential equations,...
A Mechanical system is shown in Fig. 1.1. a) Obtain a set of simultaneous integro-differential equations, in terms of velocity, to represent the system, where k is spring Constant, m is the mass and b is damper. (Hint: draw two Free Body Diagrams and obtain two equations in terms of x1 and x2 only). X1 - Ft mi m2 M TTTTTTTTYYTTTTTTTTTYYTTTTTTT Fig 1.1 b) What components and energy source do you need to use in order to build an electric...
a) [15 marks] Write the differential equations that describe the behavior of the electrical system shown...
a) [15 marks] Write the differential equations that describe the behavior of the electrical system shown in Figure 1. Assume that all electrical components behave linearly. Note that v(t) is an external input voltage signal, and vi(t) is the output voltage signal, respectively. 0000 1H 1Ω 1Ω M v(t) Figure 1. Electrical network for question 1. Use the currents ij, iz, and iz which flow through the inductors next to the red, green, and blue arrows, respectively, as the key...
Consider the mass-spring-damper system depicted in the figure below, where the input of the system is...
Consider the mass-spring-damper system depicted in the figure below, where the input of the system is the applied force F(t) and the output of the system is xít) that is the displacement of the mass according to the coordinate system defined in that figure. Assume that force F(t) is applied for t> 0 and the system is in static equilibrium before t=0 and z(t) is measured from the static equilibrium. b m F Also, the mass of the block, the...
3) The figure below shows a model including two masses and three springs. The input is...
3) The figure below shows a model including two masses and three springs. The input is an external force f(t). Important: assume that mass2 will always remain horizontal - it cannot rotate! a) Clearly state all assumptions to be used for modeling this system. b) Draw the freebody diagrams. State your "presumptions" on the configuration of the states of the system. Be sure to label the magnitude and direction of the forces consistent with those presumptions. c) Use the freebody...
Problem # 2 (50pts) m2 Find the equations of motion to describe the system below. The...
Problem # 2 (50pts) m2 Find the equations of motion to describe the system below. The spring produces zero force at zero length. The spring has zero mass, the rod has zero mass. Note: To describe the dynamics, you need 2 Generalized coordinates: 0,x. u g a) Find the velocities of the important components, mi, m2, (10 points). mi b) Find the kinetic energy of the system (10 points). c) Find the potential energy of the system (10 points). d)...
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a...
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, m) subject to a harmonic force F(t) Fo cos @t. (a) Derive the amplitudes of steady-state response for mi and m2. (b) Find the relation between k2 and m2 that leads to no steady state vibration of mi.
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, m) subject to a harmonic force...
3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the output function of the system. Assume gravity is not a factor. of the system, find the transfer f (t) C3 m2 mi Figure 1
3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the...
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
5. Figure 5 shows an electrical network, i) obtain the differential equations of the network and nofind the transfer function F(s) show that the same transfer function is obtained 12(s)/Vin(s); ii) Analyse the circuit in the s-domain and R. C i2(t) Vin(t) L Figure 5. Electrical Network 4. Find the transfer function X2(s)/F(s) of the spring-mass system shown in Figure 4. The system moves over a frictionless surface. h M2 M1 Figure 4. A 2 DOF spring-mass system over a...
Q2. A mechanical system is shown as Figure 2, where external force uz is the input and displacement y2 is the output. The force acting on m2 has a linear relationship with uj as u2=Aui. 1) List system equations; 2) Draw block diagram of the control system; 3) Build the block diagram in Simulink (screenshot and paste your diagram in your submission). ki U1 mi k2 Yi Y bi U2 V m2 y2 Figure 2
A Mechanical system is shown in Fig. 1.1. a) Obtain a set of simultaneous integro-differential equations, in terms of velocity, to represent the system, where k is spring Constant, m is the mass and b is damper. (Hint: draw two Free Body Diagrams and obtain two equations in terms of x1 and x2 only). X1 - Ft mi m2 M TTTTTTTTYYTTTTTTTTTYYTTTTTTT Fig 1.1 b) What components and energy source do you need to use in order to build an electric...
a) [15 marks] Write the differential equations that describe the behavior of the electrical system shown in Figure 1. Assume that all electrical components behave linearly. Note that v(t) is an external input voltage signal, and vi(t) is the output voltage signal, respectively. 0000 1H 1Ω 1Ω M v(t) Figure 1. Electrical network for question 1. Use the currents ij, iz, and iz which flow through the inductors next to the red, green, and blue arrows, respectively, as the key...
Consider the mass-spring-damper system depicted in the figure below, where the input of the system is the applied force F(t) and the output of the system is xít) that is the displacement of the mass according to the coordinate system defined in that figure. Assume that force F(t) is applied for t> 0 and the system is in static equilibrium before t=0 and z(t) is measured from the static equilibrium. b m F Also, the mass of the block, the...
3) The figure below shows a model including two masses and three springs. The input is an external force f(t). Important: assume that mass2 will always remain horizontal - it cannot rotate! a) Clearly state all assumptions to be used for modeling this system. b) Draw the freebody diagrams. State your "presumptions" on the configuration of the states of the system. Be sure to label the magnitude and direction of the forces consistent with those presumptions. c) Use the freebody...
Problem # 2 (50pts) m2 Find the equations of motion to describe the system below. The spring produces zero force at zero length. The spring has zero mass, the rod has zero mass. Note: To describe the dynamics, you need 2 Generalized coordinates: 0,x. u g a) Find the velocities of the important components, mi, m2, (10 points). mi b) Find the kinetic energy of the system (10 points). c) Find the potential energy of the system (10 points). d)...
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, m) subject to a harmonic force F(t) Fo cos @t. (a) Derive the amplitudes of steady-state response for mi and m2. (b) Find the relation between k2 and m2 that leads to no steady state vibration of mi.
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, m) subject to a harmonic force...
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