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QUESTION 31 Forced Undamped system, Find the general response amplitude at the chosen time for the...
Question Four (a) Determine the response x() for the undamped system subjected to the force F...
Question Four (a) Determine the response x() for the undamped system subjected to the force F as shown below and given by: ts 0.1s F(t) =-600t +120 0.1 <t s 0.2 s t> 0.2s 600t 0 The mass is initially at rest with x 0 at time 1 0. (b) Find the displacement of the mass at 1 0.25 s. k 75 N/m 0.75 kg F), N 1, S 0.2 0.1
Question Four (a) Determine the response x() for the...
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...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
1) Answer the following questions for harmonic oscillator with the given parameters and initial c...
1) Answer the following questions for harmonic oscillator with the given parameters and initial conditions Find the specific solution without converting to a linear system Convert to a linear system Find the eigenvalues and eigenvectors of the corresponding linear system Classify the oscillator (underdamped, overdamped, critically damped, undamped) (use technology to) Sketch the direction field and phase portrait Sketch the x(t)- and v(t)-graphs of the solution a. b. c. d. e. f. A) mass m-2, spring constant k 1, damping...
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
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.
1. The change of position of the center of mass of a rigid body in a mechanical system is being monitored. At time t 0, when the initial conditions of the system were x = 0.1 m and x -0m/s, a ste...
1. The change of position of the center of mass of a rigid body in a mechanical system is being monitored. At time t 0, when the initial conditions of the system were x = 0.1 m and x -0m/s, a step input of size 10 N began to apply to the system. The response of the system was represented by this differential equation: 2r + 110x + 500 x = 10 a) Write the order of the system, its...
mi Question 3. Find the general solution of the forced Mass-Spring system with the following parameters...
mi Question 3. Find the general solution of the forced Mass-Spring system with the following parameters undergoing forcing function F(t). m=2.4 kg, k=38 N/m, F(t)=1.3+3e-t/1.1 The general solution is in the form of X(t)=A1cos(wot)+A2sin(wot)+B1+B2e/11 Enter your answers for w0w0, B1B1 and B2B2 to four decimal places in the appropriate boxes below: w0:00: B1:B1: B2:B2: xlts: A
Consider the forced but undamped system described by the initial value problem 3cosuwt, (0) 0, (0...
Consider the forced but undamped system described by the initial value problem 3cosuwt, (0) 0, (0 2 (a) Determine the natural frequency of the unforced system (b) Find the solution (t) forw1 (c) Plot the solution x(t) versus t for w = 0.7, 0.8, and 0.9. (Feel free to use technology. MatLab, Mathematica, etc.) Describe how the response (t) changes as w varies in this interval. What happens as w takes values closer and closer to 1? Briefly explain why...
- Frequency Response (Amplitude Response only). Hz). with frequency, 22. for a discrete time system shown...
- Frequency Response (Amplitude Response only). Hz). with frequency, 22. for a discrete time system shown below. *(-1) - x[-2] - ... -0 and yf-1) - Y[-2] ... - x[r] - int) Find “Math Model" for the system. nt) Find "Transfer Function" for the system. Draw the pole-zero plot for the system (use unit circle on Re-Im axis) Sketch the amplitude response of the system → indicate values at important points (92 = 0, 1/4, 21/4, 37/4, T) include detailed...
Question Four (a) Determine the response x() for the undamped system subjected to the force F as shown below and given by: ts 0.1s F(t) =-600t +120 0.1 <t s 0.2 s t> 0.2s 600t 0 The mass is initially at rest with x 0 at time 1 0. (b) Find the displacement of the mass at 1 0.25 s. k 75 N/m 0.75 kg F), N 1, S 0.2 0.1
Question Four (a) Determine the response x() for the...
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...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
1) Answer the following questions for harmonic oscillator with the given parameters and initial conditions Find the specific solution without converting to a linear system Convert to a linear system Find the eigenvalues and eigenvectors of the corresponding linear system Classify the oscillator (underdamped, overdamped, critically damped, undamped) (use technology to) Sketch the direction field and phase portrait Sketch the x(t)- and v(t)-graphs of the solution a. b. c. d. e. f. A) mass m-2, spring constant k 1, damping...
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.
1. The change of position of the center of mass of a rigid body in a mechanical system is being monitored. At time t 0, when the initial conditions of the system were x = 0.1 m and x -0m/s, a step input of size 10 N began to apply to the system. The response of the system was represented by this differential equation: 2r + 110x + 500 x = 10 a) Write the order of the system, its...
mi Question 3. Find the general solution of the forced Mass-Spring system with the following parameters undergoing forcing function F(t). m=2.4 kg, k=38 N/m, F(t)=1.3+3e-t/1.1 The general solution is in the form of X(t)=A1cos(wot)+A2sin(wot)+B1+B2e/11 Enter your answers for w0w0, B1B1 and B2B2 to four decimal places in the appropriate boxes below: w0:00: B1:B1: B2:B2: xlts: A
Consider the forced but undamped system described by the initial value problem 3cosuwt, (0) 0, (0 2 (a) Determine the natural frequency of the unforced system (b) Find the solution (t) forw1 (c) Plot the solution x(t) versus t for w = 0.7, 0.8, and 0.9. (Feel free to use technology. MatLab, Mathematica, etc.) Describe how the response (t) changes as w varies in this interval. What happens as w takes values closer and closer to 1? Briefly explain why...
- Frequency Response (Amplitude Response only). Hz). with frequency, 22. for a discrete time system shown below. *(-1) - x[-2] - ... -0 and yf-1) - Y[-2] ... - x[r] - int) Find “Math Model" for the system. nt) Find "Transfer Function" for the system. Draw the pole-zero plot for the system (use unit circle on Re-Im axis) Sketch the amplitude response of the system → indicate values at important points (92 = 0, 1/4, 21/4, 37/4, T) include detailed...
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