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API A spring-mass-damper system is shown in Figure API (a). The Bode diagram obtained by experimental...
For the system shown below, a 20Kg mass is sitting on a spring-damper system on a foundation. The system is operating a...
For the system shown below, a 20Kg mass is sitting on a spring-damper system on a foundation. The system is operating at a frequency of 20 rad/s with only one unbalanced mass, m. For the maximum transmissibility at (=0.2, use the chart provided below to determine the suitable values for the spring and the damper constants If a second mass is added to the system (m2=m) at an angle 90 degrees behind the first mass, What is the maximum force...
A. 1st Order Systems Consider the spring-damper system shown in Figure 1. Figure 1: spring-damper system...
A. 1st Order Systems Consider the spring-damper system shown in Figure 1. Figure 1: spring-damper system (1)Draw FBD and deduce EOM. Clearly state your assumptions. (2)Cast EOM as an ODE in standard form; write the time constant T and the forcing function f(t) in terms of k,c, f*(1) (3) Write the solution x(t) as the sum x(t) = x (1)+x,() and do the following: a) give the name of x (1) b) write the equation that x(!) must satisfy and...
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...
The landing gear of an airplane can be idealised as the spring-mass-damper system shown in the...
The landing gear of an airplane can be idealised as the spring-mass-damper system shown in the figure below. If the runway surface is described by y() = Ycoswt, determine the value of the damping coefficient c that gives an amplitude of vibration of the airplane of 1.0 mm. Assume m 153 rad/s. 1.8 mm, and w 2200 kg, k 4.9 MN/m, Y = x(e) Housing with strut and viscous damping Mass of aircraft y(e) Runway ww.
Consider a single degree of freedom (SDOF) with mass-spring-damper system
Consider a single degree of freedom (SDOF) with mass-spring-damper system subjected to harmonic excitation having the following characteristics: Mass, m = 850 kg; stiffness, k = 80 kN/m; damping constant, c = 2000 N.s/m, forcing function amplitude, f0 = 5 N; forcing frequency, ωt = 30 rad/s. (a) Calculate the steady-state response of the system and state whether the system is underdamped, critically damped, or overdamped. (b) What happen to the steady-state response when the damping is increased to 18000 N.s/m? (Hint: Determine...
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 second order mechanical system of a mass connected to a spring and a damper is subjected to a s...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a s...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mi+ci +kx- Asin(ot) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor un-damped natural frequency on a. and the
A second order mechanical system of a...
Consider the digital control system shown in figure below. Draw a Bode diagram in the w...
Consider the digital control system shown in figure below. Draw a Bode diagram in the w plane. Set the gain K so that the phase margin becomes equal to 50°. With the gain K so set, determine the gain margin and the static velocity error constant Kv The sampling period is as sumed to be 0.1 sec, or T-0.1 ctt) -Ts rtr ss 10) Gls)
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...
For the system shown below, a 20Kg mass is sitting on a spring-damper system on a foundation. The system is operating at a frequency of 20 rad/s with only one unbalanced mass, m. For the maximum transmissibility at (=0.2, use the chart provided below to determine the suitable values for the spring and the damper constants If a second mass is added to the system (m2=m) at an angle 90 degrees behind the first mass, What is the maximum force...
A. 1st Order Systems Consider the spring-damper system shown in Figure 1. Figure 1: spring-damper system (1)Draw FBD and deduce EOM. Clearly state your assumptions. (2)Cast EOM as an ODE in standard form; write the time constant T and the forcing function f(t) in terms of k,c, f*(1) (3) Write the solution x(t) as the sum x(t) = x (1)+x,() and do the following: a) give the name of x (1) b) write the equation that x(!) must satisfy and...
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...
The landing gear of an airplane can be idealised as the spring-mass-damper system shown in the figure below. If the runway surface is described by y() = Ycoswt, determine the value of the damping coefficient c that gives an amplitude of vibration of the airplane of 1.0 mm. Assume m 153 rad/s. 1.8 mm, and w 2200 kg, k 4.9 MN/m, Y = x(e) Housing with strut and viscous damping Mass of aircraft y(e) Runway ww.
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 second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mi+ci +kx- Asin(ot) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor un-damped natural frequency on a. and the
A second order mechanical system of a...
Consider the digital control system shown in figure below. Draw a Bode diagram in the w plane. Set the gain K so that the phase margin becomes equal to 50°. With the gain K so set, determine the gain margin and the static velocity error constant Kv The sampling period is as sumed to be 0.1 sec, or T-0.1 ctt) -Ts rtr ss 10) Gls)
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...
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