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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 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...
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.
3 dismo plesis The spring mass damper system shown is subjected to a force f(t), which...
3
dismo plesis
The spring mass damper system shown is subjected to a force f(t), which is a step function. b m f(t) At time t=0, with zero initial conditions, the system is subjected to the force. The magnitude of the force is 4 newton, while the spring rate is 8.2 newton/meter, and the damping coefficient is 10 newton-sec/meter. Calculate the energy stored in the spring, in Joules, in steady state.
Answer last four questions 1. A spring-mass-damper system has mass of 150 kg, stiffness of 1500...
Answer last four questions
1. A spring-mass-damper system has mass of 150 kg, stiffness of 1500 N/m and damping coefficient of 200 kg/s. i) Calculate the undamped natural frequency ii) Calculate the damping ratio iii) Calculate the damped natural frequency iv) Is the system overdamped, underdamped or critically damped? v) Does the solution oscillate? The system above is given an initial velocity of 10 mm/s and an initial displacement of -5 mm. vi) Calculate the form of the response and...
QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if...
QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if the spring stiffness is 3000 N/m and the damping coefficient c is set at 320 Ns/m. If a periodic 260 N force is applied to the mass at a frequency of 2 Hz, determine the amplitude of the forced vibration. Spring Viscous damper 35 kg Figure 4
Question 6 (Second-order system - log decrement). A mass-spring-damper system has a mass of 100 kg....
Question 6 (Second-order system - log decrement). A mass-spring-damper system has a mass of 100 kg. Its free response amplitude decays such that the amplitude of the 30th cycle is 20% of the amplitude of the 1st cycle. It takes 60 sec to complete 30 cycles. Estimate the damping constant c and the spring constant k.
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...
A spring mass damper system is fixed at one end. The damper behaves such that a...
A spring mass damper system is fixed at one end. The damper behaves such that a constant force of 66 N applied to the damper gives a velocity of 7.95 m/second. Determine the damping constant 'c' ?
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...
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...
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...
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.
3
dismo plesis
The spring mass damper system shown is subjected to a force f(t), which is a step function. b m f(t) At time t=0, with zero initial conditions, the system is subjected to the force. The magnitude of the force is 4 newton, while the spring rate is 8.2 newton/meter, and the damping coefficient is 10 newton-sec/meter. Calculate the energy stored in the spring, in Joules, in steady state.
Answer last four questions
1. A spring-mass-damper system has mass of 150 kg, stiffness of 1500 N/m and damping coefficient of 200 kg/s. i) Calculate the undamped natural frequency ii) Calculate the damping ratio iii) Calculate the damped natural frequency iv) Is the system overdamped, underdamped or critically damped? v) Does the solution oscillate? The system above is given an initial velocity of 10 mm/s and an initial displacement of -5 mm. vi) Calculate the form of the response and...
QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if the spring stiffness is 3000 N/m and the damping coefficient c is set at 320 Ns/m. If a periodic 260 N force is applied to the mass at a frequency of 2 Hz, determine the amplitude of the forced vibration. Spring Viscous damper 35 kg Figure 4
Question 6 (Second-order system - log decrement). A mass-spring-damper system has a mass of 100 kg. Its free response amplitude decays such that the amplitude of the 30th cycle is 20% of the amplitude of the 1st cycle. It takes 60 sec to complete 30 cycles. Estimate the damping constant c and the spring constant k.
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...
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...
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