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A s Spring (k)-mass (m)- damper (c) system is subject to two impulses: F-2F and F-F escribe the d...
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.
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,...
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...
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...
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...
(By hand) Suppose a spring-mass-damper system with mass m, linear damping coefficient cand spring constant k...
(By hand) Suppose a spring-mass-damper system with mass m, linear damping coefficient cand spring constant k is subject to a force given by Equation 1 above. Determine the steady state response of the system to the above force. f(t) = 3 1-1 - 7/2 <t<o 1 0<t</2 1
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...
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...
1. A spring-mass-damper system of M =0.05 Ib.s/in, K=15 lb/in, and C =0.7 Ib.s/in is subjected...
1. A spring-mass-damper system of M =0.05 Ib.s/in, K=15 lb/in, and C =0.7 Ib.s/in is subjected to a harmonic force F(t)=30 Cos (10t) Ibf. Determine: (a) The equation of motion of the system (b) The response as function of time (c) The value of the resonance frequency (d) The transmitted force (e) The range of frequencies for which greater force would be transmitted (f) Redesign the system such that only full force is transmitted to the foundation Plt) x(+)
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.
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,...
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...
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...
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...
(By hand) Suppose a spring-mass-damper system with mass m, linear damping coefficient cand spring constant k is subject to a force given by Equation 1 above. Determine the steady state response of the system to the above force. f(t) = 3 1-1 - 7/2 <t<o 1 0<t</2 1
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...
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...
1. A spring-mass-damper system of M =0.05 Ib.s/in, K=15 lb/in, and C =0.7 Ib.s/in is subjected to a harmonic force F(t)=30 Cos (10t) Ibf. Determine: (a) The equation of motion of the system (b) The response as function of time (c) The value of the resonance frequency (d) The transmitted force (e) The range of frequencies for which greater force would be transmitted (f) Redesign the system such that only full force is transmitted to the foundation Plt) x(+)
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