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(4) What is the damping ratio fof the system? (expressed using...
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
1. Using Equations 4 and 5 determine the required natural frequency (wn) and damping ratio (7)...
1. Using Equations 4 and 5 determine the required natural frequency (wn) and damping ratio (7) that will satisfy the overshoot and rise time requirements of the controller. a. What does the natural frequency of the system quantify? i. It is the frequency at which the system tends of oscillate when continuously subjected to an external harmonic force ii. It quantifies the frequency at which the system tends to oscillate in the absence of any driving force ili. None of...
When parts of a vibrating system slide on a dry surface, the damping is:
Question 1 A vibratory system in a vehicle is to be designed with the following parameters: k= 177 N/m, C =2 N-s/m, m=23 kg. Calculate the natural frequency of damped vibration. Quèstion 2 The damping ratio for a critical damped system is: 1.0 0.5 0 1.05 Question 3 A vibratory system is defined by the following parameters: m=2 kg, k = 100N/m, C =4 N-s/m. Determine the damping factor (ε) Question 5 When parts of a vibrating system slide on a dry surface, the damping is: Viscous Coulomb Hyntoretio None of above
please answer both parts Problem 3) (21 pt) Consider a system represented by the following second...
please answer both parts
Problem 3) (21 pt) Consider a system represented by the following second order differential equation: m.*+b+*+k- x = f() a) (7 pt). If m=1, b=2, and k-16. Determine whether the system is overdamped or underdamped. Show your work. b) (7 pt) If m=2, b=24, and k=200. Find the damped frequency.
Do only parts C and D 1. A second-order system has the following transfer function that...
Do only parts C and D
1. A second-order system has the following transfer function that describes its response: F(s)- s2 +as + 9 A. For a -3, calculate the following performance specifications of the system: Natural frequency (on) Damping ratio( Estimated rise time and settling time with ±5% change (tr, ts) Estimated overshoot (MP) . B. Label (a) ±5% range of steady state, (b) tr, (c) ts, and (d) MP on the step response curve below (You may also...
Mechanical vibration subject 3. a. Consider the system of Figure 3. If C1 = C2 =...
Mechanical vibration subject
3. a. Consider the system of Figure 3. If C1 = C2 = C3 = 0, develops the equation of motion and predict the mass and stiffness matrices. Note that setting k3 = 0 in your solution should result in the stiffness matrix given by [ky + kz -k2 kz b. constructs the characteristics equation from Question 3(a) for the case m1 = 9 kg, m2 = 1 kg, k1 = 24 N/m, k2 = 3 N/m,...
IV. (5 pts). Given the feedback system shown below, with H)--1 and Gs) 5+α where a...
IV. (5 pts). Given the feedback system shown below, with H)--1 and Gs) 5+α where a and K constants. Note that H(s) represents an unstable open-loop system. We are going to determine the value of the constants that make the overall closed-loop system stable. H(s) vu) x(t) wt) G(s) 0(s) a) Find the system function, Q(s), of the closed-loop system in terms ofa and K. A quick test that you probably got the right answer: ( ONMwm.→ b) Find the...
Find the state space representation of the following system. Show all work. m2 • m1 =...
Find the state space representation of the following system. Show all work. m2 • m1 = 3 kg • m2 = 1 kg kı = 4 N/m k2 = 1 N/m C1 = 2 Ns/m C2 = 5 Ns/m C3 = 3 Ns/m
Please answer the questions for Part 1 and Part 2 showing all steps, using the provided...
Please answer the questions for Part 1 and Part 2 showing all
steps, using the provided data values.
Many thanks.
M2 2 C2 2' 2 2 C2 2'2 Spring steel Mi k1 C1 2'2 1 C1 Base y(t) Base movement Figure 2 shows a shear building with base motion. This building is modelled as a 2 DOF dynamic system where the variables of ml-3.95 kg, m2- 0.65 kg, kl-1200 N/m, k2- 68 N/m, cl- 0.40 Ns/m, c2- 0.70Ns/m The base...
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal...
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal force for some time interval f(t) = {10 sin 2t 0 0<t< y(0) 1, y'(0) -5 y"2y' 2y f(t), Tt zusor= 2. Consider two masses and three springs without no external force. The resulting force balance can be expressed as two second order ODES shown as below. mx=-(k k2)x1+ kzx2 m2x2 (k2k3)x2 + k2x1 15 If m 2,m2 ki = 1,k2 = 3, k3...
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
1. Using Equations 4 and 5 determine the required natural frequency (wn) and damping ratio (7) that will satisfy the overshoot and rise time requirements of the controller. a. What does the natural frequency of the system quantify? i. It is the frequency at which the system tends of oscillate when continuously subjected to an external harmonic force ii. It quantifies the frequency at which the system tends to oscillate in the absence of any driving force ili. None of...
please answer both parts
Problem 3) (21 pt) Consider a system represented by the following second order differential equation: m.*+b+*+k- x = f() a) (7 pt). If m=1, b=2, and k-16. Determine whether the system is overdamped or underdamped. Show your work. b) (7 pt) If m=2, b=24, and k=200. Find the damped frequency.
Do only parts C and D
1. A second-order system has the following transfer function that describes its response: F(s)- s2 +as + 9 A. For a -3, calculate the following performance specifications of the system: Natural frequency (on) Damping ratio( Estimated rise time and settling time with ±5% change (tr, ts) Estimated overshoot (MP) . B. Label (a) ±5% range of steady state, (b) tr, (c) ts, and (d) MP on the step response curve below (You may also...
Mechanical vibration subject
3. a. Consider the system of Figure 3. If C1 = C2 = C3 = 0, develops the equation of motion and predict the mass and stiffness matrices. Note that setting k3 = 0 in your solution should result in the stiffness matrix given by [ky + kz -k2 kz b. constructs the characteristics equation from Question 3(a) for the case m1 = 9 kg, m2 = 1 kg, k1 = 24 N/m, k2 = 3 N/m,...
IV. (5 pts). Given the feedback system shown below, with H)--1 and Gs) 5+α where a and K constants. Note that H(s) represents an unstable open-loop system. We are going to determine the value of the constants that make the overall closed-loop system stable. H(s) vu) x(t) wt) G(s) 0(s) a) Find the system function, Q(s), of the closed-loop system in terms ofa and K. A quick test that you probably got the right answer: ( ONMwm.→ b) Find the...
Find the state space representation of the following system. Show all work. m2 • m1 = 3 kg • m2 = 1 kg kı = 4 N/m k2 = 1 N/m C1 = 2 Ns/m C2 = 5 Ns/m C3 = 3 Ns/m
Please answer the questions for Part 1 and Part 2 showing all
steps, using the provided data values.
Many thanks.
M2 2 C2 2' 2 2 C2 2'2 Spring steel Mi k1 C1 2'2 1 C1 Base y(t) Base movement Figure 2 shows a shear building with base motion. This building is modelled as a 2 DOF dynamic system where the variables of ml-3.95 kg, m2- 0.65 kg, kl-1200 N/m, k2- 68 N/m, cl- 0.40 Ns/m, c2- 0.70Ns/m The base...
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal force for some time interval f(t) = {10 sin 2t 0 0<t< y(0) 1, y'(0) -5 y"2y' 2y f(t), Tt zusor= 2. Consider two masses and three springs without no external force. The resulting force balance can be expressed as two second order ODES shown as below. mx=-(k k2)x1+ kzx2 m2x2 (k2k3)x2 + k2x1 15 If m 2,m2 ki = 1,k2 = 3, k3...
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