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Problem 1 - Combined Systems (30pts) Consider the system shown in Figure 1 and assume that: The wheel rolls without sli...
Problem 1: The system in Figure 1 comprises two masses connected to one another through a...
Problem 1: The system in Figure 1 comprises two masses connected to one another through a spring. The block slides without friction on the support and has mass mi. The disk has radius a, mass moment of inertia I, and mass m2. The disk rolls without slipping on the support. The springs are unstretched when x(t) = x2(t) = 0. 2k 3k , m Figure 1: System for Problem 1 (a) Derive the differential equations of motion for the system...
Question 2 (Combinatorial system). For the system shown in Figure 2, the disk rolls without slipping,...
Question 2 (Combinatorial system). For the system shown in Figure 2, the disk rolls without slipping, the masses of the pulleys are negligible, and the cable is inextensible. The coordinates are defined relative to the static equilibrium position of the system. Derive the equation of motion in terms of y (mass position). X WWW Figure 2: Rotational / translational system.
Make sure to consider all parts of the problem with detail and accuracy. Please show your...
Make sure to consider all parts of the
problem with detail and accuracy. Please show your work and
explain. Thank you!
A cylindrical wheel of uniform density with mass M=11kg and radius R= 2m rolls without slipping on an incline that makes an angle of 0 = 30° with the horizontal, as shown in the diagram; there is friction between the wheel and the ramp. A block of equal mass Mis sliding on a separate, frictionless incline, also forming an...
The mass of the symmetrical wheel shown below is m = 4 kg and its radius...
The mass of the symmetrical wheel shown below is m = 4 kg and its radius of gyration about its center is kg = 0.25 m. The outer radius of the wheel is r2 = 0.4 m. The radius of the inner hub, where a cable is wrapped around it, is rı = 0.2 m. The wheel rolls without slipping. The force P, applied to the cable, is increased slowly according to the linear relation P = at, where P...
Consider the electromechanical dynamic system shown in Figure 1(a). It consists of a cart of mass...
This assignment is for my Engr dynamics systems class.
Consider the electromechanical dynamic system shown in Figure 1(a). It consists of a cart of mass m moving without slipping on a linear ground track. The cart is equipped with an armature-controlled DC motor, which is coupled to a rack and pinion mechanism to convert the rotational motion to translation and to create the driving force for the system. Figure 1(b) shows the simplified equivalent electric circuit and the mechanical model...
3) For the system shown in the figure, the input is the torque T(t) and the...
3) For the system shown in the figure, the input is the torque T(t) and the outputs are the linear displacements x(t) and the angular displacement θ(t). The equilibrium position corresponds to x 0 0. Note that there is viscous friction between the rack and the surface it slides on. Also, you may treat the small diameter shaft as massless and rigid. mr Clearly state all assumptions to be used for modeling this system. Draw the freebody diagrams. State your...
Instructions: 1. Draw the schematic of the situation described in the wording of the problem. This...
Instructions: 1. Draw the schematic of the situation described in the wording of the problem. This schematic includes a list of the data given in the wording of the problem, such as initial position (x, yo), initial velocity Ivo, V, Vol, final position (x,y), final velocity (V, V, W) or maximum height (ym). Make a decision on whether you want to use "y" or "h" for the vertical axis and keep it consistent throughout all the problems. Write down the...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s)X2 (s)/F(s) (b) Does the system oscillate with a unit step input (f (t))? Explain the reason (c) Decide if the system(x2 (t)) is stable with a unit step input (f (t))? Explain the reason 1. 320) 8 kg 2 N/m 4N-s/m 2N-s/m Fig. 1 2. There are two suspensions for a car as shown in Fig. 2 (a) Find the equations of each...
3. For experiment A, use equations 1&3 to develop a general equation for the value of...
3. For experiment A, use equations 1&3 to develop a general equation for the value of tension (T) based on the values of the two masses. You will need this later to answer lab question (4), so write it in now. 4. Based on the "net force" and "total mass" approach that was used to derive equations 3,4, and 5; develop the equation for acceleration of two masses (m, and m2) hanging vertically from either side of a frictionless pulley....
Problem 1: The system in Figure 1 comprises two masses connected to one another through a spring. The block slides without friction on the support and has mass mi. The disk has radius a, mass moment of inertia I, and mass m2. The disk rolls without slipping on the support. The springs are unstretched when x(t) = x2(t) = 0. 2k 3k , m Figure 1: System for Problem 1 (a) Derive the differential equations of motion for the system...
Question 2 (Combinatorial system). For the system shown in Figure 2, the disk rolls without slipping, the masses of the pulleys are negligible, and the cable is inextensible. The coordinates are defined relative to the static equilibrium position of the system. Derive the equation of motion in terms of y (mass position). X WWW Figure 2: Rotational / translational system.
Make sure to consider all parts of the
problem with detail and accuracy. Please show your work and
explain. Thank you!
A cylindrical wheel of uniform density with mass M=11kg and radius R= 2m rolls without slipping on an incline that makes an angle of 0 = 30° with the horizontal, as shown in the diagram; there is friction between the wheel and the ramp. A block of equal mass Mis sliding on a separate, frictionless incline, also forming an...
The mass of the symmetrical wheel shown below is m = 4 kg and its radius of gyration about its center is kg = 0.25 m. The outer radius of the wheel is r2 = 0.4 m. The radius of the inner hub, where a cable is wrapped around it, is rı = 0.2 m. The wheel rolls without slipping. The force P, applied to the cable, is increased slowly according to the linear relation P = at, where P...
This assignment is for my Engr dynamics systems class.
Consider the electromechanical dynamic system shown in Figure 1(a). It consists of a cart of mass m moving without slipping on a linear ground track. The cart is equipped with an armature-controlled DC motor, which is coupled to a rack and pinion mechanism to convert the rotational motion to translation and to create the driving force for the system. Figure 1(b) shows the simplified equivalent electric circuit and the mechanical model...
3) For the system shown in the figure, the input is the torque T(t) and the outputs are the linear displacements x(t) and the angular displacement θ(t). The equilibrium position corresponds to x 0 0. Note that there is viscous friction between the rack and the surface it slides on. Also, you may treat the small diameter shaft as massless and rigid. mr Clearly state all assumptions to be used for modeling this system. Draw the freebody diagrams. State your...
Instructions: 1. Draw the schematic of the situation described in the wording of the problem. This schematic includes a list of the data given in the wording of the problem, such as initial position (x, yo), initial velocity Ivo, V, Vol, final position (x,y), final velocity (V, V, W) or maximum height (ym). Make a decision on whether you want to use "y" or "h" for the vertical axis and keep it consistent throughout all the problems. Write down the...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s)X2 (s)/F(s) (b) Does the system oscillate with a unit step input (f (t))? Explain the reason (c) Decide if the system(x2 (t)) is stable with a unit step input (f (t))? Explain the reason 1. 320) 8 kg 2 N/m 4N-s/m 2N-s/m Fig. 1 2. There are two suspensions for a car as shown in Fig. 2 (a) Find the equations of each...
3. For experiment A, use equations 1&3 to develop a general equation for the value of tension (T) based on the values of the two masses. You will need this later to answer lab question (4), so write it in now. 4. Based on the "net force" and "total mass" approach that was used to derive equations 3,4, and 5; develop the equation for acceleration of two masses (m, and m2) hanging vertically from either side of a frictionless pulley....
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