![[1] 25 pts. A damped single degree of freedom system without applied forces is oscillating due to a certain unknown initial c](http://img.homeworklib.com/images/5a4f9d28-4842-4e96-9228-d7f75a79b7f8.png?x-oss-process=image/resize,w_560)
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[1] 25 pts. A damped single degree of freedom system without applied forces is oscillating due to...
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...
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...
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 5. (20 pts) Let ER be a positive real number and consider the damped system...
Problem 5. (20 pts) Let ER be a positive real number and consider the damped system modeled by the following second-order differential equation: y"(t) + yy' (t) + 25y(t) = 0, (a) Show that the long-term behaviour of all solutions is independent of y. (b) For which values of ye R+ does the above differential equation have oscillating solutions ? (i.e. solutions with infinitely many zeroes.) (c) Classify the above damped system into underdamped, critically damped and overdamped in terms...
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.
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...
1) Derive the 2d order differential equation for the circuit and solve the equation for a...
1) Derive the 2d order differential equation for the circuit and solve the equation for a natural response and a forced response using initial conditions. Do not use Laplace Transforms. After finding the differential equation, classify the system as critically damped, overdamped, or underdamped and derive the response equation. 12 V 20㏀ 10 mH
Problem #3 a) Determine if the next second order system is oscillating, low damped, critically damped...
Problem #3 a) Determine if the next second order system is oscillating, low damped, critically damped or overdamped. Justify your conclusion. G(s)10 s2 +s +1 b) Determine the maximum percentage overdrive (if any) and the set time to the 2% criterion that will have the response to the unit step of the previous system. c) Plot the response to the magnitude 5 step of the G (s) system.
For the system shown, (a) Determine the damping ratio (b) State whether the system is underdamped,...
For the system shown, (a) Determine the damping ratio (b) State whether the system is underdamped, critically damped, or overdamped (c) Determine x(t) or 0(t) for the given initial conditions 4 x 104 N/m 3 x 104 N/m 12.5 kg man | C 750 Ns/m x(0) = 3 cm x(O) = 0
A mass m is attached to both a spring (with given spring constant k) and a...
A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position X, and initial velocity vo Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) =C, e-pt cos (0,t-a). Also, find the undamped position function u(t) = Cocos (0,0+ - )...
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...
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 5. (20 pts) Let ER be a positive real number and consider the damped system modeled by the following second-order differential equation: y"(t) + yy' (t) + 25y(t) = 0, (a) Show that the long-term behaviour of all solutions is independent of y. (b) For which values of ye R+ does the above differential equation have oscillating solutions ? (i.e. solutions with infinitely many zeroes.) (c) Classify the above damped system into underdamped, critically damped and overdamped in terms...
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.
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...
1) Derive the 2d order differential equation for the circuit and solve the equation for a natural response and a forced response using initial conditions. Do not use Laplace Transforms. After finding the differential equation, classify the system as critically damped, overdamped, or underdamped and derive the response equation. 12 V 20㏀ 10 mH
Problem #3 a) Determine if the next second order system is oscillating, low damped, critically damped or overdamped. Justify your conclusion. G(s)10 s2 +s +1 b) Determine the maximum percentage overdrive (if any) and the set time to the 2% criterion that will have the response to the unit step of the previous system. c) Plot the response to the magnitude 5 step of the G (s) system.
For the system shown, (a) Determine the damping ratio (b) State whether the system is underdamped, critically damped, or overdamped (c) Determine x(t) or 0(t) for the given initial conditions 4 x 104 N/m 3 x 104 N/m 12.5 kg man | C 750 Ns/m x(0) = 3 cm x(O) = 0
A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position X, and initial velocity vo Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) =C, e-pt cos (0,t-a). Also, find the undamped position function u(t) = Cocos (0,0+ - )...
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