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Question8 n the spring-mass-damper system in Figure 8, the force F, is applied to the mass and it...
A force transduce r is a mass-spring-damper system. When an external force is applied to the...
A force transduce r is a mass-spring-damper system. When an external force is applied to the mass, the spring displacement is measured that indirectly represents the level of the force. The system dynamics is 8 7 (a) Convert the system dynamics into the standard form +2wnx Kownf by calculating the values of Ko-, ah in terms of the physical parameters M, B, K. (8%) (b) Calculate the transmissyde)l, force. (Hint: write down the transfer function first.) (7%) missibility Trere o...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
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...
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...
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)...
A s Spring (k)-mass (m)- damper (c) system is subject to two impulses: F-2F and F-F escribe the d...
A s Spring (k)-mass (m)- damper (c) system is subject to two impulses: F-2F and F-F escribe the displacement of the mass as a function of time in terms of m,c, k, o, and the constants in the applied force? Assume it is an underdamped system.
A s Spring (k)-mass (m)- damper (c) system is subject to two impulses: F-2F and F-F escribe the displacement of the mass as a function of time in terms of m,c, k, o, and...
3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following seco...
3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following second order linear ODE: dx,2 dt n dt2 (0) C dt where is the damping ratio an wn is the natural frequency, both related to k, b, and m (the spring constant, damping coefficient, and mass, respectively) (a) Use the forward difference approximations of (b) Using Δt andd to obtain a finite difference formula for x(t+ 2Δ) (like we did in class for the...
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,...
Problem 1. Consider the following mass, spring, and damper system. Let the force F be the...
Problem 1. Consider the following mass, spring, and damper system. Let the force F be the input and the position x be the output. M-1 kg b- 10 N s/m k 20 N/nm F = 1 N when t>=0 PART UNIT FEEDBACK CONTROL SYSTEM 5) Construct a unit feedback control for the mass-spring-damper system 6) Draw the block diagram of the unit feedback control system 7) Find the Transfer Function of the closed-loop (CL) system 8) Find and plot the...
Consider a mass-spring-damper system whose motion is described by the following system of differe...
Consider a mass-spring-damper system whose motion is described by the following system of differentiat equations [c1(f-k)+k,(f-х)-c2(x-9), f=f(t), y:' y(t) with x=x( t), where the function fit) is the input displacement function (known), while xit) and yt) are the two generalized coordinates (both unknown) of the mass-spring-damper systenm. 1. Identify the type of equations (e.g. H/NH, ODE/PDE, L/NL, order, type of coefficients, etc.J. 2. Express this system of differential equations in matrix form, assume f 0 and then determine its general...
A force transduce r is a mass-spring-damper system. When an external force is applied to the mass, the spring displacement is measured that indirectly represents the level of the force. The system dynamics is 8 7 (a) Convert the system dynamics into the standard form +2wnx Kownf by calculating the values of Ko-, ah in terms of the physical parameters M, B, K. (8%) (b) Calculate the transmissyde)l, force. (Hint: write down the transfer function first.) (7%) missibility Trere o...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
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...
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...
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)...
A s Spring (k)-mass (m)- damper (c) system is subject to two impulses: F-2F and F-F escribe the displacement of the mass as a function of time in terms of m,c, k, o, and the constants in the applied force? Assume it is an underdamped system.
A s Spring (k)-mass (m)- damper (c) system is subject to two impulses: F-2F and F-F escribe the displacement of the mass as a function of time in terms of m,c, k, o, and...
3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following second order linear ODE: dx,2 dt n dt2 (0) C dt where is the damping ratio an wn is the natural frequency, both related to k, b, and m (the spring constant, damping coefficient, and mass, respectively) (a) Use the forward difference approximations of (b) Using Δt andd to obtain a finite difference formula for x(t+ 2Δ) (like we did in class for the...
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,...
Problem 1. Consider the following mass, spring, and damper system. Let the force F be the input and the position x be the output. M-1 kg b- 10 N s/m k 20 N/nm F = 1 N when t>=0 PART UNIT FEEDBACK CONTROL SYSTEM 5) Construct a unit feedback control for the mass-spring-damper system 6) Draw the block diagram of the unit feedback control system 7) Find the Transfer Function of the closed-loop (CL) system 8) Find and plot the...
Consider a mass-spring-damper system whose motion is described by the following system of differentiat equations [c1(f-k)+k,(f-х)-c2(x-9), f=f(t), y:' y(t) with x=x( t), where the function fit) is the input displacement function (known), while xit) and yt) are the two generalized coordinates (both unknown) of the mass-spring-damper systenm. 1. Identify the type of equations (e.g. H/NH, ODE/PDE, L/NL, order, type of coefficients, etc.J. 2. Express this system of differential equations in matrix form, assume f 0 and then determine its general...
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