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2. Consider the system shown. x(t) frictionless wheels Write the EOM for the system. Note that x(...
Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input to...
Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input torque is supplied by an electric motor Specifically, T(t) T(t) -Kamp Vin(t) where 1) "Vin is the input voltage supplied to the motor N-m 2) "Kamp" is the motor gain (this constant has units of Volt) So, the transfer function for this system is (s)Kamp The moment of inertia is known...
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 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...
A. 1st Order Systems Consider the spring-damper system shown in Figure 1. Figure 1: spring-damper system...
A. 1st Order Systems Consider the spring-damper system shown in Figure 1. Figure 1: spring-damper system (1)Draw FBD and deduce EOM. Clearly state your assumptions. (2)Cast EOM as an ODE in standard form; write the time constant T and the forcing function f(t) in terms of k,c, f*(1) (3) Write the solution x(t) as the sum x(t) = x (1)+x,() and do the following: a) give the name of x (1) b) write the equation that x(!) must satisfy and...
Question 1-4 is about the following mechanical system: Data: ki-20 [N/m] b-2 [Ns/m] k2# 10 [N/m] m2 At) mi Question 1 X...
Question 1-4 is about the following mechanical system: Data: ki-20 [N/m] b-2 [Ns/m] k2# 10 [N/m] m2 At) mi Question 1 X1(s) Develop the symbolic transfer function G1(s)2 F(s) 1.1 Determine the differential equation, that this transfer function describe 1.2 Question 2 Sketch the step response for G1(s), using Matlab and explain the process 2.1 Sketch the pole /zero diagram for the transfer function G1(s) and reflect on the relation between the step response and the pole /zero diagram 2.2...
(40pts) The suspension system for one wheel of a pickup truck is illustrated in the following...
(40pts) The suspension system for one wheel of a pickup truck is illustrated in the following figure. The mass of the vehicle distributed on this wheel is mi and the mass of the wheel is m2. The suspension spring has a spring constant kı and the tire has a spring constant of k2. The damping constant of the shock absorber is b. Assume the truck's vertical displacement yi(t) is the output and the road surface profile x(t) is the input....
QUESTION 4 This question will reinforce how the Bode plot provides the steady-state response for ...
QUESTION 4 This question will reinforce how the Bode plot provides the steady-state response for a linear system in response to a sinusoidal input. Consider this forced mass-spring-damper system: Let M 6, B-48, K-72 Part a) As you did for HW 1, determine steady-state solution "x,()" when FC) 3120 cos(4b) Part b) Determine the transfer function Part c) The Bode plots for the transfer function of Part b are provided in this handout. with the parameter values of Part a....
Consider the unity-feedback system shown below: R(s) E(s) input: r(t), output: y(t) C(s) P(s) error: e()...
Consider the unity-feedback system shown below: R(s) E(s) input: r(t), output: y(t) C(s) P(s) error: e() r(t) y(t) closed-loop transfer-function: Hyr(sD t the closed-loop transfer-function be Hyr(s) Y (s) R(s) Let the transfer-function of the plant be P(s) 10 s (s 1) (s 5) The open-loop transfer-function is G(s) P(s) C(s) DESIGN OBJECTIVES: Find a controller C(s) such that the following are satisfied i) The closed-loop system is stable. ii) The steady-state error ess due to a unit-ramp input r(t)...
Problem 4. Convolve the following input X(t) with the system impulse response h(t) and plot the...
Problem 4. Convolve the following input X(t) with the system impulse response h(t) and plot the system output y(t). h(t) Problem 5. Construct a Bode plot of the input impedance DMM 100nF zin - 300F CM 500 ohms
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...
Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input torque is supplied by an electric motor Specifically, T(t) T(t) -Kamp Vin(t) where 1) "Vin is the input voltage supplied to the motor N-m 2) "Kamp" is the motor gain (this constant has units of Volt) So, the transfer function for this system is (s)Kamp The moment of inertia is known...
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...
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...
A. 1st Order Systems Consider the spring-damper system shown in Figure 1. Figure 1: spring-damper system (1)Draw FBD and deduce EOM. Clearly state your assumptions. (2)Cast EOM as an ODE in standard form; write the time constant T and the forcing function f(t) in terms of k,c, f*(1) (3) Write the solution x(t) as the sum x(t) = x (1)+x,() and do the following: a) give the name of x (1) b) write the equation that x(!) must satisfy and...
Question 1-4 is about the following mechanical system: Data: ki-20 [N/m] b-2 [Ns/m] k2# 10 [N/m] m2 At) mi Question 1 X1(s) Develop the symbolic transfer function G1(s)2 F(s) 1.1 Determine the differential equation, that this transfer function describe 1.2 Question 2 Sketch the step response for G1(s), using Matlab and explain the process 2.1 Sketch the pole /zero diagram for the transfer function G1(s) and reflect on the relation between the step response and the pole /zero diagram 2.2...
(40pts) The suspension system for one wheel of a pickup truck is illustrated in the following figure. The mass of the vehicle distributed on this wheel is mi and the mass of the wheel is m2. The suspension spring has a spring constant kı and the tire has a spring constant of k2. The damping constant of the shock absorber is b. Assume the truck's vertical displacement yi(t) is the output and the road surface profile x(t) is the input....
QUESTION 4 This question will reinforce how the Bode plot provides the steady-state response for a linear system in response to a sinusoidal input. Consider this forced mass-spring-damper system: Let M 6, B-48, K-72 Part a) As you did for HW 1, determine steady-state solution "x,()" when FC) 3120 cos(4b) Part b) Determine the transfer function Part c) The Bode plots for the transfer function of Part b are provided in this handout. with the parameter values of Part a....
Consider the unity-feedback system shown below: R(s) E(s) input: r(t), output: y(t) C(s) P(s) error: e() r(t) y(t) closed-loop transfer-function: Hyr(sD t the closed-loop transfer-function be Hyr(s) Y (s) R(s) Let the transfer-function of the plant be P(s) 10 s (s 1) (s 5) The open-loop transfer-function is G(s) P(s) C(s) DESIGN OBJECTIVES: Find a controller C(s) such that the following are satisfied i) The closed-loop system is stable. ii) The steady-state error ess due to a unit-ramp input r(t)...
Problem 4. Convolve the following input X(t) with the system impulse response h(t) and plot the system output y(t). h(t) Problem 5. Construct a Bode plot of the input impedance DMM 100nF zin - 300F CM 500 ohms
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...
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