Determine the equivalent damping coefficient for the following nonlinear damper:
where C1 = 5 N s/m and C3 = 0.6 N s3 /m3 .
Note: the damper is to be operated around a speed of 5 m/s.
Homework Answers
Solution:
The relation between force and velocity is given by
The equivalent damping coefficient is given by,
Substitute,
Therefore,
Add Answer to:
Determine the equivalent damping coefficient for the following
nonlinear damper:
where C1 = 5 N s/m...
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5) Rayleigh's dissipation function for a stand-alone viscous damper element with damping coefficient of c is defined as D = {ci?. In the presence of viscous damping, the system's EOMs can be found by a modified Lagrange's equations as (0) - d al al ad + dt ağK дак дäk Where L=T-V, T and V are the total kinetic and potential energies of the system, respectively, and Qx is the generalized force due to enternal forcing projected to k-th DOF....
Please write legibly Consider an ideal mass-spring-damper system similar to Figure 3.2. Find the damping coefficient of the system if a mass of 380 g is used in combination with a spring with stif...
Please write legibly
Consider an ideal mass-spring-damper system similar to Figure 3.2. Find the damping coefficient of the system if a mass of 380 g is used in combination with a spring with stiffness k = 17 N/m and a period of 0.945 s. If the system is released from rest 5 cm from it's equilibrium point at to = 0 s, find the trajectory of the position of the mass-spring-damper from it's release until t 3s Figure 3.2: Mass-spring-damper...
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 2 Write a Matlab code* (script) or use Excel to determine the damping coefficient of...
PROBLEM 2 Write a Matlab code* (script) or use Excel to determine the damping coefficient of a spring - mass - damper system with a mass of 165 kg and stiffness of 2400 N/m such that its response will die out (decay) after about 1.5 s, given a zero initial position and an initial velocity of 8 mm/s. 1. Display the numerical value of the damping coefficient. 2. Plot the response of the system. *Turn in your Matlab code with...
(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
Problem 1 Vcc Consider the following Capacitor Network: C1 C3 GND C1 2.2p C3-3.3μ F C,...
Problem 1 Vcc Consider the following Capacitor Network: C1 C3 GND C1 2.2p C3-3.3μ F C, 400nF Let VAB12 V (Note: m-"milli", μ-"micro", n " nano", p "pico", & f ,, "femto") (3 Points) Calculate the Equivalent Capacitance, f (3 Points) Calculate the Charge, 0, on C . (3 Points) Calculate the Voltage, V, at Terminal J (with respect to Ground)
F(N) 2. A 15 kg oscillator with a stiffness of k = 960 N/m and damping...
F(N) 2. A 15 kg oscillator with a stiffness of k = 960 N/m and damping coefficient c = 60 Ns/m is driven by a square- wave excitation F(t) shown in the figure. Determine and plot the steady state response for 12 s using 100 terms in the Fourier series solution. 100 -100
6-B) A weight attached to a spring of stiffness 982 N/m has a viscous damping device....
6-B) A weight attached to a spring of stiffness 982 N/m has a viscous damping device. When the weight is displaced and released, the period of vibration is 1.02 s, and the magnitude of consecutive amplitudes is 0.61 m and 0.29 m. a) Identify the mass (m) and damping (c) coefficient. b) Determine the amplitude and phase of the response when a force, f(t) = 4.2 cos (6.31) N, acts on the system.
For a mass-spring-damper mechanical systems shown below, x200) K1-1 N/m 0000 -X,(0) K-1 N/m 00004 =...
For a mass-spring-damper mechanical systems shown below, x200) K1-1 N/m 0000 -X,(0) K-1 N/m 00004 = 1 N-s/m fr2 M1=1 kg = 2 N-s/m M2 -1 kg 13 = 1 N-s/m 1. Find the differential equations relating input force f(t) and output displacement xi(t) and x2(C) in the system. (40 marks) (Hint: K, fy and M are spring constant, friction coefficient and mass respectively) 2. Determine the transfer function G(s)= X1(s)/F(s) (20 marks)
5. Consider the model of a spring-mass-damper system, where the following parameter values are as...
5. Consider the model of a spring-mass-damper system, where the following parameter values are assumed: m 1,b 2, k 2 a. Design a rate feedback controller to meet the following step response specifictions: ts 1 s, ζ 206. b. Compare the step response of the closed-loop systems in Probs. 3&5
5. Consider the model of a spring-mass-damper system, where the following parameter values are assumed: m 1,b 2, k 2 a. Design a rate feedback controller to meet the following...
5) Rayleigh's dissipation function for a stand-alone viscous damper element with damping coefficient of c is defined as D = {ci?. In the presence of viscous damping, the system's EOMs can be found by a modified Lagrange's equations as (0) - d al al ad + dt ağK дак дäk Where L=T-V, T and V are the total kinetic and potential energies of the system, respectively, and Qx is the generalized force due to enternal forcing projected to k-th DOF....
Please write legibly
Consider an ideal mass-spring-damper system similar to Figure 3.2. Find the damping coefficient of the system if a mass of 380 g is used in combination with a spring with stiffness k = 17 N/m and a period of 0.945 s. If the system is released from rest 5 cm from it's equilibrium point at to = 0 s, find the trajectory of the position of the mass-spring-damper from it's release until t 3s Figure 3.2: Mass-spring-damper...
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 2 Write a Matlab code* (script) or use Excel to determine the damping coefficient of a spring - mass - damper system with a mass of 165 kg and stiffness of 2400 N/m such that its response will die out (decay) after about 1.5 s, given a zero initial position and an initial velocity of 8 mm/s. 1. Display the numerical value of the damping coefficient. 2. Plot the response of the system. *Turn in your Matlab code with...
(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
Problem 1 Vcc Consider the following Capacitor Network: C1 C3 GND C1 2.2p C3-3.3μ F C, 400nF Let VAB12 V (Note: m-"milli", μ-"micro", n " nano", p "pico", & f ,, "femto") (3 Points) Calculate the Equivalent Capacitance, f (3 Points) Calculate the Charge, 0, on C . (3 Points) Calculate the Voltage, V, at Terminal J (with respect to Ground)
F(N) 2. A 15 kg oscillator with a stiffness of k = 960 N/m and damping coefficient c = 60 Ns/m is driven by a square- wave excitation F(t) shown in the figure. Determine and plot the steady state response for 12 s using 100 terms in the Fourier series solution. 100 -100
6-B) A weight attached to a spring of stiffness 982 N/m has a viscous damping device. When the weight is displaced and released, the period of vibration is 1.02 s, and the magnitude of consecutive amplitudes is 0.61 m and 0.29 m. a) Identify the mass (m) and damping (c) coefficient. b) Determine the amplitude and phase of the response when a force, f(t) = 4.2 cos (6.31) N, acts on the system.
For a mass-spring-damper mechanical systems shown below, x200) K1-1 N/m 0000 -X,(0) K-1 N/m 00004 = 1 N-s/m fr2 M1=1 kg = 2 N-s/m M2 -1 kg 13 = 1 N-s/m 1. Find the differential equations relating input force f(t) and output displacement xi(t) and x2(C) in the system. (40 marks) (Hint: K, fy and M are spring constant, friction coefficient and mass respectively) 2. Determine the transfer function G(s)= X1(s)/F(s) (20 marks)
5. Consider the model of a spring-mass-damper system, where the following parameter values are assumed: m 1,b 2, k 2 a. Design a rate feedback controller to meet the following step response specifictions: ts 1 s, ζ 206. b. Compare the step response of the closed-loop systems in Probs. 3&5
5. Consider the model of a spring-mass-damper system, where the following parameter values are assumed: m 1,b 2, k 2 a. Design a rate feedback controller to meet the following...
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