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Q.3 A two-degree of freedom torsional system shown below is subjected to initial excitation 0,(0) 0,...
State vIIU F(0) 3) (25 pts.) Find the response of an undamped single degree of freedom systerm to the excitation F(t...
State vIIU F(0) 3) (25 pts.) Find the response of an undamped single degree of freedom systerm to the excitation F(t) shown on the right using the convolution integral. cos 21 to
State vIIU F(0) 3) (25 pts.) Find the response of an undamped single degree of freedom systerm to the excitation F(t) shown on the right using the convolution integral. cos 21 to
2. Consider the torsional system shown in Figure 2. Assume damping is negligible, i.e., ok/J. Fro...
2. Consider the torsional system shown in Figure 2. Assume damping is negligible, i.e., ok/J. From the free vibration response, it is observed that the natural frequency of the system is w Then increase the moment of inertia of the disk to JJ, and the free vibration response shows that the natural frequency is reduced to a,2. Calculate J and k Express Jand k in terms of ω 1 and ω". Hint: Apply a, = vk/J to both cases. 0,T...
NOTE: this is base excitation not force vibration. 1: For the single degree of freedom system...
NOTE: this is base excitation not
force vibration.
1: For the single degree of freedom system driven by a harmonic base motion we discussed in the class. The governing equation is given by mž + ci + kx = cy + ky Where y(t) = Y sin wt and w is the driving (excitation) frequency. Given the initial conditions are x(0) = x, and (0) = v.. Combine the homogeneous and particular solutions and satisfy the initial conditions to obtain...
Consider the single degree-of-freedom (DOF) dynamic system whose EOM is shown below: a. Find the natural...
Consider the single degree-of-freedom (DOF) dynamic system whose EOM is shown below: a. Find the natural frequency, damping ratio, and stiffness. b. Find the complete response when the initial conditions are y(0) 0, (0)-1 c. Compare the answers from mathematical software (eg. Matlab or Mathematica). Plot the responses from 0 to 10 seconds (both displacement and velocity) with the software. Append the software codes.
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)=...
13. Briefly describe how a two degree of freedom system can be made to vibrate in one of its pure...
13. Briefly describe how a two degree of freedom system can be made to vibrate in one of its pure modes. sャ 2. (a) Sketch the amplitude ratio and phase angle for damping of 0.01 and 0.3, and indicate the peak amplitude values. Name the axes with correct numerica (b) Compare this amplitude diagram with a similar one that corresponds to base excitation, emphasizing t a single degree of freedom system subjected to harmonic force with phasizing the differences (15)...
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...
3(a). Find the equations of motion for the system shown below. The system is two degree...
3(a). Find the equations of motion for the system shown below. The system is two degree of freedom system with degrees of freedom X, and X2. Please find two equations of motion for this dynamical system by both Newtons method and Euler Lagrange. The point with which the spring is attached with the wall has zero displacement indeed) x X2 m2 ki kr Frictionless surfaces on which masses are resting Springs can be assumed to be massless Formulas: Formula to...
Plz ASAP written clearly. 1. The system shown is is subjected to the base-excitation Determine a)...
Plz
ASAP written clearly.
1. The system shown is is subjected to the base-excitation Determine a) the equation of motion b) the response of the system C. c) displacement transmissibility Take K 600 Tb/in, M-6 Ib.s/in, C 3 Ib.sVin [Show all your work
For a single degree of freedom system whose motion is defined by x(0), what is the...
For a single degree of freedom system whose motion is defined by x(0), what is the angle between the response x(t) and the response i(0? Between the response x() and the response o?
State vIIU F(0) 3) (25 pts.) Find the response of an undamped single degree of freedom systerm to the excitation F(t) shown on the right using the convolution integral. cos 21 to
State vIIU F(0) 3) (25 pts.) Find the response of an undamped single degree of freedom systerm to the excitation F(t) shown on the right using the convolution integral. cos 21 to
2. Consider the torsional system shown in Figure 2. Assume damping is negligible, i.e., ok/J. From the free vibration response, it is observed that the natural frequency of the system is w Then increase the moment of inertia of the disk to JJ, and the free vibration response shows that the natural frequency is reduced to a,2. Calculate J and k Express Jand k in terms of ω 1 and ω". Hint: Apply a, = vk/J to both cases. 0,T...
NOTE: this is base excitation not
force vibration.
1: For the single degree of freedom system driven by a harmonic base motion we discussed in the class. The governing equation is given by mž + ci + kx = cy + ky Where y(t) = Y sin wt and w is the driving (excitation) frequency. Given the initial conditions are x(0) = x, and (0) = v.. Combine the homogeneous and particular solutions and satisfy the initial conditions to obtain...
Consider the single degree-of-freedom (DOF) dynamic system whose EOM is shown below: a. Find the natural frequency, damping ratio, and stiffness. b. Find the complete response when the initial conditions are y(0) 0, (0)-1 c. Compare the answers from mathematical software (eg. Matlab or Mathematica). Plot the responses from 0 to 10 seconds (both displacement and velocity) with the software. Append the software codes.
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)=...
13. Briefly describe how a two degree of freedom system can be made to vibrate in one of its pure modes. sャ 2. (a) Sketch the amplitude ratio and phase angle for damping of 0.01 and 0.3, and indicate the peak amplitude values. Name the axes with correct numerica (b) Compare this amplitude diagram with a similar one that corresponds to base excitation, emphasizing t a single degree of freedom system subjected to harmonic force with phasizing the differences (15)...
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...
3(a). Find the equations of motion for the system shown below. The system is two degree of freedom system with degrees of freedom X, and X2. Please find two equations of motion for this dynamical system by both Newtons method and Euler Lagrange. The point with which the spring is attached with the wall has zero displacement indeed) x X2 m2 ki kr Frictionless surfaces on which masses are resting Springs can be assumed to be massless Formulas: Formula to...
Plz
ASAP written clearly.
1. The system shown is is subjected to the base-excitation Determine a) the equation of motion b) the response of the system C. c) displacement transmissibility Take K 600 Tb/in, M-6 Ib.s/in, C 3 Ib.sVin [Show all your work
For a single degree of freedom system whose motion is defined by x(0), what is the angle between the response x(t) and the response i(0? Between the response x() and the response o?
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