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For the single DOF spring-mass-damper system shown, the displacement of the mass is x. Assume m-...
Problem 2 - A modified mass-spring-damper system: Model the modified mass-spring-damper system shown below. The mass...
Problem 2 - A modified mass-spring-damper system: Model the modified mass-spring-damper system shown below. The mass of the handle is negligi- ble (only 1 FBD is necessary). Consider the displacement (t) to be the input to the system and the cart displacement az(t) to be the output. You may assume negligible drag. MwSpring-Damper System M0 Problem 3 Repeat problem 2, but with the following differences: • Assume the mass of the handle m, is not equal to zero. You may...
On a ECP Rectilinear Plant (1 DOF system) mass-spring-damper system, I am given the transfer func...
On a ECP Rectilinear Plant (1 DOF system) mass-spring-damper system, I am given the transfer function as: 1/(M*s^2 + B*s + K). With values mass M = 0.67538 kg, friction coefficient B = 1.8951 Ns/M, spring constant K = 322.278 N/M, and Damping coefficient d=2.54821 Ns/m. I know the Open loop system model is: (1/(0.6738s^2 + 1.89515s + 322.278)) = (1.481/(s^2+2.806s+4.772)) Implement a simple controller using only one mass (+spring + damper) so the control is critically damped
On a ECP Rectilinear Plant (1 DOF system) mass-spring-damper system, I am given the transfer function...
On a ECP Rectilinear Plant (1 DOF system) mass-spring-damper system, I am given the transfer function as: 1/(M*s^2 + B*s + K). With values mass M = 0.67538 kg, friction coefficient B = 1.8951 Ns/M, spring constant K = 322.278 N/M, and Damping coefficient d=2.54821 Ns/m. I know the Open loop system model is: (1/(0.6738s^2 + 1.89515s + 322.278)) = (1.481/(s^2+2.806s+4.772)) Implement a simple controller using only one mass (+spring + damper) so the control is critically damped
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
Problem 1 (Harmonic Oscillators) A mass-damper-spring system is a simple harmonic oscillator whose dynamics is governed...
Problem 1 (Harmonic Oscillators) A mass-damper-spring system is a simple harmonic oscillator whose dynamics is governed by the equation of motion where m is the mass, c is the damping coefficient of the damper, k is the stiffness of the spring, F is the net force applied on the mass, and x is the displacement of the mass from its equilibrium point. In this problem, we focus on a mass-damper-spring system with m = 1 kg, c-4 kg/s, k-3 N/m,...
63 Figure P6.3 shows a mass-damper system (no stiffness, Problem 2.3). Displacement x is measured...
63 Figure P6.3 shows a mass-damper system (no stiffness, Problem 2.3). Displacement x is measured from an equilibrium position where the damper is at the "neutral" position. The external force () is a short-duration pulse function: f(!)-5N for 0SS002 s, and f,() = 0 for t > 0.02 s. The system parameters are mass m-0.5kg and viscous friction coefficient b 3 N-s/m and the system is initially at rest. Usc Simulink to determine the system response and plot displacement xit)...
(20pts) Consider the vertical spring-mass-damper system shown below, where m 2 kg, b 4 N-s/m, and...
(20pts) Consider the vertical spring-mass-damper system shown below, where m 2 kg, b 4 N-s/m, and k 20N/m. Assume that x(0) 0.1 m and (0) 0. The displacement is measured form the equilibrium position. Derive a mathematical model of the system (i.e. an ODE). Then find x(t) as a function of time t.
Problem 4. Consider the spring-mass system shown in the figure. The displacement of the mass m...
Problem 4. Consider the spring-mass system shown in the figure. The displacement of the mass m as a function of time is as follows: x = Xocoswt) + cos(Wnt) ωη where xo is the initial displacement equals to 0.1 m, čo is the initial velocity equals to 1 m/s, and Wr is the natural frequency of the system equals to 4 rad/s. Calculate the acceleration (second time derivative of displacement) of the mass after 1 s with a time step...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at the right end of the spring k3 and x() is the displacement of mass ml. (Note that the input is displacement, NOT force) k3 k1 m2 (a) (10pts) Draw necessary free-body diagrams, and the governing equations of motion of the system. (b) (10pts) Find the transfer function from the input u() to the output x(t). (c) (10pts) Given the system parameter values of m1-m2-1,...
A vibration isolation system for a 1-DOF mechanical system is shown below. Displacement of the mass...
A vibration isolation system for a 1-DOF mechanical system is shown below. Displacement of the mass x is measured from the static equilibrium position and the system parameters are m = 0.3 kg. k=10N/m, b = 4.4 Ns/m, and by = 0.5 Ns/m. Fixed 1. TI W Fixed base Figure / sehen voulon tem a) Derive the mathematical model of the system. Make sure you have the FBD and all equations and signs are properly showcased. b) Use the system...
Problem 2 - A modified mass-spring-damper system: Model the modified mass-spring-damper system shown below. The mass of the handle is negligi- ble (only 1 FBD is necessary). Consider the displacement (t) to be the input to the system and the cart displacement az(t) to be the output. You may assume negligible drag. MwSpring-Damper System M0 Problem 3 Repeat problem 2, but with the following differences: • Assume the mass of the handle m, is not equal to zero. You may...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
Problem 1 (Harmonic Oscillators) A mass-damper-spring system is a simple harmonic oscillator whose dynamics is governed by the equation of motion where m is the mass, c is the damping coefficient of the damper, k is the stiffness of the spring, F is the net force applied on the mass, and x is the displacement of the mass from its equilibrium point. In this problem, we focus on a mass-damper-spring system with m = 1 kg, c-4 kg/s, k-3 N/m,...
63 Figure P6.3 shows a mass-damper system (no stiffness, Problem 2.3). Displacement x is measured from an equilibrium position where the damper is at the "neutral" position. The external force () is a short-duration pulse function: f(!)-5N for 0SS002 s, and f,() = 0 for t > 0.02 s. The system parameters are mass m-0.5kg and viscous friction coefficient b 3 N-s/m and the system is initially at rest. Usc Simulink to determine the system response and plot displacement xit)...
(20pts) Consider the vertical spring-mass-damper system shown below, where m 2 kg, b 4 N-s/m, and k 20N/m. Assume that x(0) 0.1 m and (0) 0. The displacement is measured form the equilibrium position. Derive a mathematical model of the system (i.e. an ODE). Then find x(t) as a function of time t.
Problem 4. Consider the spring-mass system shown in the figure. The displacement of the mass m as a function of time is as follows: x = Xocoswt) + cos(Wnt) ωη where xo is the initial displacement equals to 0.1 m, čo is the initial velocity equals to 1 m/s, and Wr is the natural frequency of the system equals to 4 rad/s. Calculate the acceleration (second time derivative of displacement) of the mass after 1 s with a time step...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at the right end of the spring k3 and x() is the displacement of mass ml. (Note that the input is displacement, NOT force) k3 k1 m2 (a) (10pts) Draw necessary free-body diagrams, and the governing equations of motion of the system. (b) (10pts) Find the transfer function from the input u() to the output x(t). (c) (10pts) Given the system parameter values of m1-m2-1,...
A vibration isolation system for a 1-DOF mechanical system is shown below. Displacement of the mass x is measured from the static equilibrium position and the system parameters are m = 0.3 kg. k=10N/m, b = 4.4 Ns/m, and by = 0.5 Ns/m. Fixed 1. TI W Fixed base Figure / sehen voulon tem a) Derive the mathematical model of the system. Make sure you have the FBD and all equations and signs are properly showcased. b) Use the system...
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