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Given an underdamped single-degree-of-freedom system with m 10 kg. c = 20 Ns/m. k = 4000...
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...
Problem 2 (25 points): Consider an undamped single-degree-of-freedom system with k = 10 N/m, 41 =...
Problem 2 (25 points): Consider an undamped single-degree-of-freedom system with k = 10 N/m, 41 = 10 N 92 = 8N, and m = 10 kg subjected to the harmonic force f(t) = qı sin(vt) + 92 cos(vt), v = 1 rad/ sec. Assume zero initial conditions (0) = 0 and c(0) = 0. Derive and plot the analytical solution of the displacement of the system. mm m = f(t) WWWWWWWW No friction Problem 2 Problem 3 (30 points): Using...
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
Model for Evaluation The model used for evaluation is the single degree of freedom lumped mass mo...
Model for Evaluation The model used for evaluation is the single degree of freedom lumped mass model defined by second order differential equation with constant coefficients. This model is shown in Figure 1. x(t)m m f(t) Figure 1 - Single Degree of Freedom Model The equation of motion describing this system can easily be shown to be md-x + cdx + kx = f(t) dt dt where m is the mass, c is the damping and k is the stiffness...
[1] 25 pts. A damped single degree of freedom system without applied forces is oscillating due to...
solve for #2
[1] 25 pts. A damped single degree of freedom system without applied forces is oscillating due to a certain unknown initial conditions. Derive a response equation x(t) for the following four cases. a. 5 pts. 0 (no damping) b. 10 pts. 0<1 (underdamped) c. 5 pts. >1 (overdamped) d. 5 pts. ๕-1 (critically damped) Here the is the damping ratio of the oscillating system. [2] 5 pts. For the same system of underdamped case with initial conditions...
using matlab The damping system has a single degree of freedom as follows: dx2 dx m++...
using matlab
The damping system has a single degree of freedom as follows: dx2 dx m++ kx = + kx = F(t) dt dt The second ordinary differential equation can be divided to two 1st order differential equation as: dx dx F с k x1 = = x2 ,X'2 X2 -X1 dt dt m m m m N F = 10, m = 5 kg k = 40, and the damping constant = 0.1 The initial conditions are [0 0]...
solve by matlab The damping system has a single degree of freedom as follows: dx2 dx...
solve by matlab
The damping system has a single degree of freedom as follows: dx2 dx mo++ kx = F(t) dt dt The second ordinary differential equation can be divided to two 1sorder differential equation as: dx dx F C k xí -X2 -X1 dt dt m m m = x2 ,x'z m N F = 10, m = 5 kg k = 40, and the damping constant = 0.1 The initial conditions are [00] and the time interval is...
3. Consider the following mass-spring-damper system. Let m= 1 kg, b = 10 Ns/m, and k...
3. Consider the following mass-spring-damper system. Let m= 1 kg, b = 10 Ns/m, and k = 20 N/m. b m F k a) Derive the open-loop transfer function X(S) F(s) Plot the step response using matlab. b) Derive the closed-loop transfer function with P-controller with Kp = 300. Plot the step response using matlab. c) Derive the closed-loop transfer function with PD-controller with Ky and Ka = 10. Plot the step response using matlab. d) Derive the closed-loop transfer...
Consider the following single degree of freedom mass-spring damper system with m=1 kg, c=3 N.s/m, and...
Consider the following single degree of freedom mass-spring damper system with m=1 kg, c=3 N.s/m, and k=2N/m. The system is at rest when a force 5e-3t is applied. By using the concept of the Lagrange Transform (using partial fractions), obtain the response, x(t) of the system.
3) For the single degree of freedom system shown below: a) Use the equivalent system method...
3) For the single degree of freedom system shown below: a) Use the equivalent system method to derive the differential equation governing the motion of the system, taking χ as the Slender har of mass m generalized coordinate. Rigid 1 link b) If m-6 kg, M = 10 kg, and k=500 N/m, determine the value of c that makes the system critically damped. c) For the values obtained in part (b), determine the response of the system, x(t) if x(0)=...
Problem 2 (25 points): Consider an undamped single-degree-of-freedom system with k = 10 N/m, 41 = 10 N 92 = 8N, and m = 10 kg subjected to the harmonic force f(t) = qı sin(vt) + 92 cos(vt), v = 1 rad/ sec. Assume zero initial conditions (0) = 0 and c(0) = 0. Derive and plot the analytical solution of the displacement of the system. mm m = f(t) WWWWWWWW No friction Problem 2 Problem 3 (30 points): Using...
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
Model for Evaluation The model used for evaluation is the single degree of freedom lumped mass model defined by second order differential equation with constant coefficients. This model is shown in Figure 1. x(t)m m f(t) Figure 1 - Single Degree of Freedom Model The equation of motion describing this system can easily be shown to be md-x + cdx + kx = f(t) dt dt where m is the mass, c is the damping and k is the stiffness...
solve for #2
[1] 25 pts. A damped single degree of freedom system without applied forces is oscillating due to a certain unknown initial conditions. Derive a response equation x(t) for the following four cases. a. 5 pts. 0 (no damping) b. 10 pts. 0<1 (underdamped) c. 5 pts. >1 (overdamped) d. 5 pts. ๕-1 (critically damped) Here the is the damping ratio of the oscillating system. [2] 5 pts. For the same system of underdamped case with initial conditions...
using matlab
The damping system has a single degree of freedom as follows: dx2 dx m++ kx = + kx = F(t) dt dt The second ordinary differential equation can be divided to two 1st order differential equation as: dx dx F с k x1 = = x2 ,X'2 X2 -X1 dt dt m m m m N F = 10, m = 5 kg k = 40, and the damping constant = 0.1 The initial conditions are [0 0]...
solve by matlab
The damping system has a single degree of freedom as follows: dx2 dx mo++ kx = F(t) dt dt The second ordinary differential equation can be divided to two 1sorder differential equation as: dx dx F C k xí -X2 -X1 dt dt m m m = x2 ,x'z m N F = 10, m = 5 kg k = 40, and the damping constant = 0.1 The initial conditions are [00] and the time interval is...
3. Consider the following mass-spring-damper system. Let m= 1 kg, b = 10 Ns/m, and k = 20 N/m. b m F k a) Derive the open-loop transfer function X(S) F(s) Plot the step response using matlab. b) Derive the closed-loop transfer function with P-controller with Kp = 300. Plot the step response using matlab. c) Derive the closed-loop transfer function with PD-controller with Ky and Ka = 10. Plot the step response using matlab. d) Derive the closed-loop transfer...
3) For the single degree of freedom system shown below: a) Use the equivalent system method to derive the differential equation governing the motion of the system, taking χ as the Slender har of mass m generalized coordinate. Rigid 1 link b) If m-6 kg, M = 10 kg, and k=500 N/m, determine the value of c that makes the system critically damped. c) For the values obtained in part (b), determine the response of the system, x(t) if x(0)=...
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