Differential this vibration equation from dynamic vibration absorber (dva) system. if x2 is the output of...
9. Explain how we can design a vibration absorber which mitigates the vibration of the systems shown in Fig 2. Fo sin ot Machine (mi) x1(t) Isolator (k1/2) Isolator (k12) Rigid base Dynamic vibration absorber Figure 2: 2 DOF system
9. Explain how we can design a vibration absorber which mitigates the vibration of the systems shown in Fig 2. Fo sin ot Machine (mi) x1(t) Isolator (k1/2) Isolator (k12) Rigid base Dynamic vibration absorber Figure 2: 2 DOF system
1. Figure 1 shows a dynamic vibration absorber, which is used in many applications involving n the vibration of machines with unbalanced components. Obtain the differential equations niido nolvto work describing the system k ON TM (0)d MY k2 howien Isnoaleug My y2 noi nutetens brit 9Tugi worla metayaeds to (2), N(2),V Figure 1. Diagram of a vibration absorber Find the transfer functions relating Xo(s) and Xin (s) for the systems shown in Figure 2 and 2. Figure 3. Xin...
5. A two-input, two-output dynamic system is defined by the following differential equations system 2x, (t) ) +3x1(t) -2x2 () fi(t) x2 t) -2x,(t) +2x2(t) f2(t) Determine its transfer function matrix considering that the input is (fi (t) f2(t) and the output is x, (t) x2 (t)J.
5. A two-input, two-output dynamic system is defined by the following differential equations system 2x, (t) ) +3x1(t) -2x2 () fi(t) x2 t) -2x,(t) +2x2(t) f2(t) Determine its transfer function matrix considering that...
Problems 47 2.56. Determine the differential equation of motion for free vibration of the system shown in Fig. P2.56, using virtual work m/ft FIGURE P2.56
Problems 47 2.56. Determine the differential equation of motion for free vibration of the system shown in Fig. P2.56, using virtual work m/ft FIGURE P2.56
6. An underdamped shock absorber for a moon-buggy is to be designed. The system can be considered as simple SDOF system weighing 2500 N as shown in Figure 2 (a) and its damped free vibration response is shown in Figure 2 (b).lf the damped period of vibration is to be 0.8 sec and the amplitude x, is to be reduced to one-third in one half cycle. A/2 a. Draw the free-body and kinetic diagrams for the system. b. Determine the...
Assume a dynamic
system is described by the following ordinary differential equation
(ODE)
1. Assume a dynamic system is described by the following ordinary differential equation (ODE): y(4) + 9y(3) + 30ij + 429 + 20y F(t) = where y = (r' y /dt'.. (a) (10 %) Let F(t) = 1 for t 0, please solve the ODE analytically. (b) (10 %) Please give a brief comment to the evolution of the system. (c) (5 %) Please give a brief...
Given the two dynamic systems S2 a ER Si has state r1, control u, and output y. S2 has state (x2, r3), control w and output z. (a) Draw a dynamic diagram of system S2 (b) Express the equations for S1 and S2 in matrix from and determine whether each system is controllable, observable. (c) These two systems are connected in series with w-y. The resulting system is called S3. Write down the matrix form of the equation for S3...
6 720 SECTION B- Attempt any TWO Questions from this Section. 4 An air compressor experiences excessive vibrations when running at 1100 rpm. It is fitted with a tuned dynamic absorber in order to reduce these vibrations. The mass of the compressor, me, is 80 kg and the total stiffness of its supports, kc, is 1075 kN/m. The amplitude of the out of balance force, P, is 30 N The compressor with the absorber in place is shown in Figure...
2. The output of a system is given by the differential equation below: Determine the free respqnse y(t) of the system for y(0)-1 and y(0) = 0. Determine the forced response y(t) of the system for a unit impulse input. y + 4y +29y F(t) a. b.
Consider a two-tank system, where x, is the level of the first tank, and x2 is the level of the second tank. This dynamic system is described by the -xj-x2. The output to be Q4. following model: dt controlled is the level of the second tank. (a)Write down the state-space model in matrix form. Verify the 20% (b)Design a state feedback controller so that the closed-loop poles are 25% controllability of the system located at -3 and -4 (c) The...