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.
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Find the total response of a single-DOF system with m
= 10 kg, c = 20...
Given an underdamped single-degree-of-freedom system with m 10 kg. c = 20 Ns/m. k = 4000...
Given an underdamped single-degree-of-freedom system with m 10 kg. c = 20 Ns/m. k = 4000 N/m. Assuming zero initial conditions Xo-Xo-0. response of the system to a unit step function f(t) - 1. itcx +Kx) steady-state value of the unit step response.
12 The frequency response of a single DOF system of mass 4 kg is given as shown. If the stiffness...
12 The frequency response of a single DOF system of mass 4 kg is given as shown. If the stiffness of the system is doubled and it is subjected to a periodic force F) 200sin60r N, determine the maximum steady state response of the system 10 2 30 10 15 20 25 , rad/sec
12 The frequency response of a single DOF system of mass 4 kg is given as shown. If the stiffness of the system is doubled and...
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
Q.1 (35 pts) Find the response of a single degree of freedom system with m=10kg, c=20N-5/m,...
Q.1 (35 pts) Find the response of a single degree of freedom system with m=10kg, c=20N-5/m, K-4000N/m, when subjected to an external force F(t)=100Cos(ot) a. Amplitude of vibrations when o=10 rad's b. Phase difference when 0-10 rad/s C. The frequency of disturbing force corresponding to resonance d. The amplitude of vibrations at resonance frequency.
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...
Problem 2) For a 2 DOF system the equations of motion are given as: m9 [m...
Problem 2) For a 2 DOF system the equations of motion are given as: m9 [m OX -M29 2 m29 0 mal -29 Where m=m2 Em g -gravity and L =length a) Determine the frequencies and mode shapes. b) Verify that the natural modes are orthogonal. c) Determine the response (0) (0)) Note: xi(t) = XO, xa(t) = 0 and 1) = xo.* () = 0 d) If the system is excited by a harmonic force F. (t) =F, sinot,...
QUESTION 31 Forced Undamped system, Find the general response amplitude at the chosen time for the...
QUESTION 31 Forced Undamped system, Find the general response amplitude at the chosen time for the given system parameters: m= 2 kg k = 200 N/m • Initial Conditions: Xo = 0.005 m to = 0.5 • Initial amplitude of the external force, 10 N • Excitation's frequency w 4 rad/sec m Find x(t) t = 10 sec, x(t = 10) = Take Test: Test Part-2 VULUTUIN Find the response amplitude at the chosen time for the given system parameters:...
Problem 2 (20%) Free Vibration with Velocity Dependent Force. Consider a 1 DOF system consisting of...
Problem 2 (20%) Free Vibration with Velocity Dependent Force. Consider a 1 DOF system consisting of a block with mass 2 kg hanging from a spring with stiffness 100 N/m. The block is fully immersed in the liquid and based on the properties of the liquid, you have determined experimentally that the drag force (damping force) on the block has a magnitude of 0.91*] where x is velocity and 0.9 has units (Ns/m). Assume positive displacement of the block is...
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.
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using...
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using 1he convolution Q.1 An nderdamped system is subjected to a transient force the system given the following data: m 10 kg. k 1000 N/m, integral, (b) sketch the response. F(t) 50 (1
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using 1he convolution Q.1 An nderdamped system is subjected to a transient force the system given the...
Given an underdamped single-degree-of-freedom system with m 10 kg. c = 20 Ns/m. k = 4000 N/m. Assuming zero initial conditions Xo-Xo-0. response of the system to a unit step function f(t) - 1. itcx +Kx) steady-state value of the unit step response.
12 The frequency response of a single DOF system of mass 4 kg is given as shown. If the stiffness of the system is doubled and it is subjected to a periodic force F) 200sin60r N, determine the maximum steady state response of the system 10 2 30 10 15 20 25 , rad/sec
12 The frequency response of a single DOF system of mass 4 kg is given as shown. If the stiffness of the system is doubled and...
Q.1 (35 pts) Find the response of a single degree of freedom system with m=10kg, c=20N-5/m, K-4000N/m, when subjected to an external force F(t)=100Cos(ot) a. Amplitude of vibrations when o=10 rad's b. Phase difference when 0-10 rad/s C. The frequency of disturbing force corresponding to resonance d. The amplitude of vibrations at resonance frequency.
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...
Problem 2) For a 2 DOF system the equations of motion are given as: m9 [m OX -M29 2 m29 0 mal -29 Where m=m2 Em g -gravity and L =length a) Determine the frequencies and mode shapes. b) Verify that the natural modes are orthogonal. c) Determine the response (0) (0)) Note: xi(t) = XO, xa(t) = 0 and 1) = xo.* () = 0 d) If the system is excited by a harmonic force F. (t) =F, sinot,...
QUESTION 31 Forced Undamped system, Find the general response amplitude at the chosen time for the given system parameters: m= 2 kg k = 200 N/m • Initial Conditions: Xo = 0.005 m to = 0.5 • Initial amplitude of the external force, 10 N • Excitation's frequency w 4 rad/sec m Find x(t) t = 10 sec, x(t = 10) = Take Test: Test Part-2 VULUTUIN Find the response amplitude at the chosen time for the given system parameters:...
Problem 2 (20%) Free Vibration with Velocity Dependent Force. Consider a 1 DOF system consisting of a block with mass 2 kg hanging from a spring with stiffness 100 N/m. The block is fully immersed in the liquid and based on the properties of the liquid, you have determined experimentally that the drag force (damping force) on the block has a magnitude of 0.91*] where x is velocity and 0.9 has units (Ns/m). Assume positive displacement of the block is...
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.
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using 1he convolution Q.1 An nderdamped system is subjected to a transient force the system given the following data: m 10 kg. k 1000 N/m, integral, (b) sketch the response. F(t) 50 (1
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using 1he convolution Q.1 An nderdamped system is subjected to a transient force the system given the...
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