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For a single degree of freedom system whose motion is defined by x(0), what is the...
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)=...
3. Consider the equation of motion of a single-degree-of-freedom system: mi + ci + kx =...
3. Consider the equation of motion of a single-degree-of-freedom system: mi + ci + kx = F(1) Derive the condition that leads to divergent oscillations in each of the following cases: (a) when the forcing function is proportional to the displacement, F(t) = F,x(t); when the forcing function is proportional to the velocity, F(t) = Fox(t); and (c) when the forcing function is proportional to the acceleration, F(t) = F,x(t).
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.
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...
[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...
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...
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...
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.
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
Q.3 A two-degree of freedom torsional system shown below is subjected to initial excitation 0,(0) 0,...
Q.3 A two-degree of freedom torsional system shown below is subjected to initial excitation 0,(0) 0, 02(0) 2, 0,(0) 2, 02 (0)= 0. Plot the response of the system. Assume I 1 and GJ L 1 L GJ GJ
Q.3 A two-degree of freedom torsional system shown below is subjected to initial excitation 0,(0) 0, 02(0) 2, 0,(0) 2, 02 (0)= 0. Plot the response of the system. Assume I 1 and GJ L 1 L GJ GJ
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)=...
3. Consider the equation of motion of a single-degree-of-freedom system: mi + ci + kx = F(1) Derive the condition that leads to divergent oscillations in each of the following cases: (a) when the forcing function is proportional to the displacement, F(t) = F,x(t); when the forcing function is proportional to the velocity, F(t) = Fox(t); and (c) when the forcing function is proportional to the acceleration, F(t) = F,x(t).
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.
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...
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...
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...
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.
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
Q.3 A two-degree of freedom torsional system shown below is subjected to initial excitation 0,(0) 0, 02(0) 2, 0,(0) 2, 02 (0)= 0. Plot the response of the system. Assume I 1 and GJ L 1 L GJ GJ
Q.3 A two-degree of freedom torsional system shown below is subjected to initial excitation 0,(0) 0, 02(0) 2, 0,(0) 2, 02 (0)= 0. Plot the response of the system. Assume I 1 and GJ L 1 L GJ GJ
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