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12 The frequency response of a single DOF system of mass 4 kg is given as shown. If the stiffness...
Find the total response of a single-DOF system with m = 10 kg, c = 20...
Find the total response of a single-DOF system with m
= 10 kg, c = 20 N-s/m, k = 4000 N/m, xo =
0.01m and v0 = 0 when an external force F(t) = 400cos(5t) acts on
the system.
Assignment 2 1. Find the total response of a single-DOF system with m = 10 kg, c = 20 N-s/m, k = 4000 N/m, x, = 0.01m and Vo=0 when an external force F(t) = 400cos(51) acts on 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 single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300...
A single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300 Ns/m, and spring constant of 5000 N/m, is subjected to periodic displacement excitation u(t) as shown in the figure below. 1. Derive the equation of motion 2. Using Laplace transform, find characteristic equation. 3. Find the undamped and damped natural frequencies. 4. Find the damping ratio. 5. Find the transfer function of output x(t) to the periodic input u(t) using Laplace transform.
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...
Olt) 1422LLA 1. The system at the right is subject to the harmonic + x(t) force...
Olt) 1422LLA 1. The system at the right is subject to the harmonic + x(t) force f(t) = Fo sin ot as shown, with amplitude 50 N and a forcing frequency due to a motor (not m shown) with speed = 191 rotations per minute (RPM). Mass m can only translate horizontally and the rod is pinned at point O. The parameters are: r = 5 cm, m= 10 kg, Jo = 1 kg m-, kı = 1000 N/m, ka...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
Find the analytical solution for the response of the following viscously damped 1 DOF system subjected...
Find the analytical solution for the response of the following viscously damped 1 DOF system subjected to a force F(t)=Fcos(wt) Governing equation: mx(double dot) + cx(dot) + kx = F(t) w = 1 rad/sec Fo = 3 to= 0 m= 1kg c = 0.125 kg/s k = 1 N/m initial conditions: x0 = 2, x(dot)o = 0 Time increments are considered 0.1, 0.05, and 0.01 tE(0,70) User the FDM central method. RUnge-kutta method and analytical solution and compare your results
Question # 1: [25%] The system in the figure, m= 4 kg, a = 2 m,...
Question # 1: [25%] The system in the figure, m= 4 kg, a = 2 m, b= 3 m, k = 2500 N/m, c= 30 N.s/m, is subjected to a force excitation F(t)= F, sin(ot), where F = 1000 N. Find the maximum steady-state displacement of the mass for each of the following case: 1. The excitation frequency, o, is in the rage of 0-3 Hz. 2. The excitation frequency, o, is in the rage of 3-10 Hz 3. The...
Vibrations (don’t have pic) There is a 1-DOF system that has mass 1 kg, spring stiffness...
Vibrations (don’t have pic) There is a 1-DOF system that has mass 1 kg, spring stiffness 100 N/m. Q: Free vibration was done to the system and the magnitude of the vibration decreased by 10% per period. How much is the damping coefficient?
question will save this response. Questo Question 10 10 points A mass mis suspended from a...
question will save this response. Questo Question 10 10 points A mass mis suspended from a spring of stiffness 403 N/m, with natural frequency 30 rad/s. It is subjected to harmonic force of 1.73 N and having a forcing frequency of 7 rad's. Find the maximum amplitude of the forced motion of the mass in meters.
Find the total response of a single-DOF system with m
= 10 kg, c = 20 N-s/m, k = 4000 N/m, xo =
0.01m and v0 = 0 when an external force F(t) = 400cos(5t) acts on
the system.
Assignment 2 1. Find the total response of a single-DOF system with m = 10 kg, c = 20 N-s/m, k = 4000 N/m, x, = 0.01m and Vo=0 when an external force F(t) = 400cos(51) acts on 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 single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300 Ns/m, and spring constant of 5000 N/m, is subjected to periodic displacement excitation u(t) as shown in the figure below. 1. Derive the equation of motion 2. Using Laplace transform, find characteristic equation. 3. Find the undamped and damped natural frequencies. 4. Find the damping ratio. 5. Find the transfer function of output x(t) to the periodic input u(t) using Laplace transform.
Olt) 1422LLA 1. The system at the right is subject to the harmonic + x(t) force f(t) = Fo sin ot as shown, with amplitude 50 N and a forcing frequency due to a motor (not m shown) with speed = 191 rotations per minute (RPM). Mass m can only translate horizontally and the rod is pinned at point O. The parameters are: r = 5 cm, m= 10 kg, Jo = 1 kg m-, kı = 1000 N/m, ka...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
Question # 1: [25%] The system in the figure, m= 4 kg, a = 2 m, b= 3 m, k = 2500 N/m, c= 30 N.s/m, is subjected to a force excitation F(t)= F, sin(ot), where F = 1000 N. Find the maximum steady-state displacement of the mass for each of the following case: 1. The excitation frequency, o, is in the rage of 0-3 Hz. 2. The excitation frequency, o, is in the rage of 3-10 Hz 3. The...
question will save this response. Questo Question 10 10 points A mass mis suspended from a spring of stiffness 403 N/m, with natural frequency 30 rad/s. It is subjected to harmonic force of 1.73 N and having a forcing frequency of 7 rad's. Find the maximum amplitude of the forced motion of the mass in meters.
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