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For a mass-spring-damper mechanical systems shown below, x200) K1-1 N/m 0000 -X,(0) K-1 N/m 00004 =...
For the single DOF spring-mass-damper system shown, the displacement of the mass is x. Assume m-...
For the single DOF spring-mass-damper system shown, the displacement of the mass is x. Assume m- 1 kg, c 1 N-s/m, k = 1 N/m, and f(t)-1 N for all time. If the initial displacement and velocity of the mass are zero, then based on the central difference numerical integration method as discussed in the notes, using an integration time step of h 0.5 s, what is the displacement of the mass at t 0.5 s? In other words, what...
Question8 n the spring-mass-damper system in Figure 8, the force F, is applied to the mass and it...
Question8 n the spring-mass-damper system in Figure 8, the force F, is applied to the mass and its displacement is measured via r(t), whilst k and c are the spring and damper constants, respectively x(t) Figure 8: A spring-mass-damper system. a) Obtain the differential equation that relates the input force F, to the measured dis- (6 marks) placement x(t) for the system in Figure 8. b) Draw the block diagram representation of the system in Figure 8. c) Based on...
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.
A quarter-car suspension model consisting of a spring and a damper is shown in Figure 1....
A quarter-car suspension model consisting of a spring and a damper is shown in Figure 1. An active suspension element produces an input force F. Draw a free-body diagram for the sprung mass m, and hence derive a differential equation relating the input force F to the sprung mass displacement x. (a) (5 marks) (b) Assuming a mass m-250kg, spring coefficient k 100Nm-1 and damping coefficient of c-50Nsm1, show that the transfer function from the input force F to the...
The mechanical system shown in the figure below is excited by a sinusoidal force f(t)-Fi cos(ut...
The mechanical system shown in the figure below is excited by a sinusoidal force f(t)-Fi cos(ut + ?) N. The differential equation of the displacement x(t) is Use phasor techniques to solve for the displacement phasor Xin terms of the excitation frequency ? , and the mechanical elements M = 0.1 kg, D = 8 N-s/m , and K = 2,000 N/m . If Fi-10 N and ?? = 30°, determine the excitation frequency w (in rad/s) at which 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,...
(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.
4. Consider the mechanical system shown below with a spring with stiffness, k (N/m), in parallel...
4. Consider the mechanical system shown below with a spring with stiffness, k (N/m), in parallel with a viscous damper with coefficient, h (Nós/m) and an externally applied force, Fexi(t) (N). u(t) a. Find the equation that relates the applied force, Fext(t) and the displacement, u(t). b. If the spring component has a stiffness of k = 75 N/m, the damper component has coefficient h = 50 N s/m and the externally applied force is a constant 4.5 N applied...
1) A railroad car of mass 2,000 kg traveling at a velocity v = 10 m/s...
1) A railroad car of mass 2,000 kg traveling at a velocity v = 10 m/s is stopped at the end of the tracks by a spring-damper system, as shown below. If the stiffness of the spring is k= 40 N/mm and the damping constant c 20 N-s/mm, determine (a) the maximum displacement of the car after engaging the springs and damper, (b) the time taken to reach maximum displacement k2 P 0000 k/2
1) A railroad car of mass...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical system subjected to fluctuations (t) at the wall is provided in figure 2. Spring k, is interconnected with both spring ka and damper Os at the nodal point. The independent displacement of mass m is denoted by 1, the independent displacement of mass m, is denoted by r2, and the independent displacement of the node is denoted by ra. Assume a linear force-displacement/velocity relationship...
For the single DOF spring-mass-damper system shown, the displacement of the mass is x. Assume m- 1 kg, c 1 N-s/m, k = 1 N/m, and f(t)-1 N for all time. If the initial displacement and velocity of the mass are zero, then based on the central difference numerical integration method as discussed in the notes, using an integration time step of h 0.5 s, what is the displacement of the mass at t 0.5 s? In other words, what...
Question8 n the spring-mass-damper system in Figure 8, the force F, is applied to the mass and its displacement is measured via r(t), whilst k and c are the spring and damper constants, respectively x(t) Figure 8: A spring-mass-damper system. a) Obtain the differential equation that relates the input force F, to the measured dis- (6 marks) placement x(t) for the system in Figure 8. b) Draw the block diagram representation of the system in Figure 8. c) Based on...
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.
A quarter-car suspension model consisting of a spring and a damper is shown in Figure 1. An active suspension element produces an input force F. Draw a free-body diagram for the sprung mass m, and hence derive a differential equation relating the input force F to the sprung mass displacement x. (a) (5 marks) (b) Assuming a mass m-250kg, spring coefficient k 100Nm-1 and damping coefficient of c-50Nsm1, show that the transfer function from the input force F to the...
The mechanical system shown in the figure below is excited by a sinusoidal force f(t)-Fi cos(ut + ?) N. The differential equation of the displacement x(t) is Use phasor techniques to solve for the displacement phasor Xin terms of the excitation frequency ? , and the mechanical elements M = 0.1 kg, D = 8 N-s/m , and K = 2,000 N/m . If Fi-10 N and ?? = 30°, determine the excitation frequency w (in rad/s) at which 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,...
(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.
4. Consider the mechanical system shown below with a spring with stiffness, k (N/m), in parallel with a viscous damper with coefficient, h (Nós/m) and an externally applied force, Fexi(t) (N). u(t) a. Find the equation that relates the applied force, Fext(t) and the displacement, u(t). b. If the spring component has a stiffness of k = 75 N/m, the damper component has coefficient h = 50 N s/m and the externally applied force is a constant 4.5 N applied...
1) A railroad car of mass 2,000 kg traveling at a velocity v = 10 m/s is stopped at the end of the tracks by a spring-damper system, as shown below. If the stiffness of the spring is k= 40 N/mm and the damping constant c 20 N-s/mm, determine (a) the maximum displacement of the car after engaging the springs and damper, (b) the time taken to reach maximum displacement k2 P 0000 k/2
1) A railroad car of mass...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical system subjected to fluctuations (t) at the wall is provided in figure 2. Spring k, is interconnected with both spring ka and damper Os at the nodal point. The independent displacement of mass m is denoted by 1, the independent displacement of mass m, is denoted by r2, and the independent displacement of the node is denoted by ra. Assume a linear force-displacement/velocity relationship...
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