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Consider the mechandral system shown in 99 Q 2 oblar the dofferential canation that describe The...
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended ...
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended from springs with spring constants ki and k, respectively. Assume that there is no damping in the system. a) Show that the displacements z1 and 2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above resuit to show that the spring-mass system satisfies the following fourth order differential equation. and ) Find the general solution...
Problem1: Consider the translational system shown in the figure below. Att-0,x (displacement)-y (...
Problem1: Consider the translational system shown in the figure below. Att-0,x (displacement)-y (let y represents velocity)-fat)0. The physical constants are: M-3,B1,B2B 0.5. Find the first order system equation in y and do following. a) Find the response, y(t) of the system when subjected to a step input,falt)-A b). Find time constant, "7". c Identify the steady state, "yss" and transient, "yr" part of the response. d). Sketch the complete response when the input is unit step function. e). Is the...
Consider the system shown. Let m-1; m2-2, k-4,b-2,p 5sin (3t) X1(s) a) Find the transfer functions...
Consider the system shown. Let m-1; m2-2, k-4,b-2,p 5sin (3t) X1(s) a) Find the transfer functions G1(s) - b) Find the steady state outputs x1ss(s), x2(s) X2(s) F(s) pt) mi 112 m2 1s
Consider the multi-degree of freedom system shown in Fig 1. Let the first four spring constants...
Consider the multi-degree of freedom system shown in Fig 1. Let the first four spring constants k; = 1 N/m {i=1,..4}, the final spring constant be kg = 2 N/m, the exterior masses mi = m = 3 kg, and the interior masses m2 = m3 = 1 kg. Jovit cum alv Lampu Milli MÁV DLİNE Derive the set of scalar equations of motion of the system, written in ma- trix/vector form.
H (8) Fig. Q1 Q2 [20 Marks] a) Consider the mechanical system shown in Fig. 22....
H (8) Fig. Q1 Q2 [20 Marks] a) Consider the mechanical system shown in Fig. 22. (i) Obtain the differential equations that describe the system. [4 Marks] (ii) Obtain the state variable matrix that represents the system. [4 Marks] V2 i w m2 -16.JPG here to search O
7. Consider the mechanical system shown below. The system initially at rest. The displacements u, y,...
7. Consider the mechanical system shown below. The system initially at rest. The displacements u, y, and z are measured from their respective rest positions. Given that u is the input, y is the output, 1) Obtain the transfer function of the system (20pt). 2) Obtain a state-space representation of the system (20pt). I b, - obteranlara k, 12 WI
(30pts) Consider the liquid level system shown in the figure. Assume the outflow rate Q (m3/s) th...
(30pts) Consider the liquid level system shown in the figure. Assume the outflow rate Q (m3/s) through the outflow value is related to the liquid level H by Assume also that, when the inflow rate Qi and outflow rate QOare at Q = 0015m3/s, the liquid level stays at constant H. The capacitance C of the tank is 2m2 Find the steady state value of the liquid level system H. Develop the governing equations for the liquid level system and...
Problem # 1 (b): Obtain a mathematical model of the system shown below. Problem1: Consider the ...
Problem # 1 (b): Obtain a mathematical model of the system shown below. Problem1: Consider the system shown below which is at rest for t<0. Assume the displacement x is the output of the system and is measured from the equilibrium position. Att-0, the cart is given initial conditions x(0)- xo and dx(0ydt v Obtain the output motion x0)Assume that m-10 kg, b-50 N-s/m, b-70 N-sm, -400 N/m, k2- 600 N/m. da diagam c.rditinstoo)20 추dx(Hat20.5m/s inilia) Problem12i Referring to Problem...
5. (10 points) Consider the liquid-level system shown. At steady state, the inflow rate is Q:...
5. (10 points) Consider the liquid-level system shown. At steady state, the inflow rate is Q: the outflow rates are Q1 and Q, respectively; the flow rate from tank 1 to tank 2 is Q12, and the heads of tanks 1 and 2 are H and H2, respectively. If the inflow rate is changed from Q to Q+q, determine the transfer function Hz(8)/Q(s). Assume the deviations 4,91,92,912, h, and hy are all small. 6th Jan Hathe +7 т/ н+А, JE>,+8....
Mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/...
mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/m, and k 20 N/m and that input force u is a constant force of 5 N, obtain the response of the sys- tem. Plot the response curves n(t) versus r and y2(t) versus t with MATLAB Problem B-5-23 Consider the system shown in Figure 5-45. The system is at rest for t < 0. The dis placements...
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended from springs with spring constants ki and k, respectively. Assume that there is no damping in the system. a) Show that the displacements z1 and 2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above resuit to show that the spring-mass system satisfies the following fourth order differential equation. and ) Find the general solution...
Problem1: Consider the translational system shown in the figure below. Att-0,x (displacement)-y (let y represents velocity)-fat)0. The physical constants are: M-3,B1,B2B 0.5. Find the first order system equation in y and do following. a) Find the response, y(t) of the system when subjected to a step input,falt)-A b). Find time constant, "7". c Identify the steady state, "yss" and transient, "yr" part of the response. d). Sketch the complete response when the input is unit step function. e). Is the...
Consider the system shown. Let m-1; m2-2, k-4,b-2,p 5sin (3t) X1(s) a) Find the transfer functions G1(s) - b) Find the steady state outputs x1ss(s), x2(s) X2(s) F(s) pt) mi 112 m2 1s
Consider the multi-degree of freedom system shown in Fig 1. Let the first four spring constants k; = 1 N/m {i=1,..4}, the final spring constant be kg = 2 N/m, the exterior masses mi = m = 3 kg, and the interior masses m2 = m3 = 1 kg. Jovit cum alv Lampu Milli MÁV DLİNE Derive the set of scalar equations of motion of the system, written in ma- trix/vector form.
H (8) Fig. Q1 Q2 [20 Marks] a) Consider the mechanical system shown in Fig. 22. (i) Obtain the differential equations that describe the system. [4 Marks] (ii) Obtain the state variable matrix that represents the system. [4 Marks] V2 i w m2 -16.JPG here to search O
7. Consider the mechanical system shown below. The system initially at rest. The displacements u, y, and z are measured from their respective rest positions. Given that u is the input, y is the output, 1) Obtain the transfer function of the system (20pt). 2) Obtain a state-space representation of the system (20pt). I b, - obteranlara k, 12 WI
(30pts) Consider the liquid level system shown in the figure. Assume the outflow rate Q (m3/s) through the outflow value is related to the liquid level H by Assume also that, when the inflow rate Qi and outflow rate QOare at Q = 0015m3/s, the liquid level stays at constant H. The capacitance C of the tank is 2m2 Find the steady state value of the liquid level system H. Develop the governing equations for the liquid level system and...
Problem # 1 (b): Obtain a mathematical model of the system shown below. Problem1: Consider the system shown below which is at rest for t<0. Assume the displacement x is the output of the system and is measured from the equilibrium position. Att-0, the cart is given initial conditions x(0)- xo and dx(0ydt v Obtain the output motion x0)Assume that m-10 kg, b-50 N-s/m, b-70 N-sm, -400 N/m, k2- 600 N/m. da diagam c.rditinstoo)20 추dx(Hat20.5m/s inilia) Problem12i Referring to Problem...
5. (10 points) Consider the liquid-level system shown. At steady state, the inflow rate is Q: the outflow rates are Q1 and Q, respectively; the flow rate from tank 1 to tank 2 is Q12, and the heads of tanks 1 and 2 are H and H2, respectively. If the inflow rate is changed from Q to Q+q, determine the transfer function Hz(8)/Q(s). Assume the deviations 4,91,92,912, h, and hy are all small. 6th Jan Hathe +7 т/ н+А, JE>,+8....
mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/m, and k 20 N/m and that input force u is a constant force of 5 N, obtain the response of the sys- tem. Plot the response curves n(t) versus r and y2(t) versus t with MATLAB Problem B-5-23 Consider the system shown in Figure 5-45. The system is at rest for t < 0. The dis placements...
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