A two degree of freedomundamped system has naturalfrequencies 2 rad/s and 3 rad/sand corresponding mode shapes{{{ and . A damping ratioof 2% is assumed for bothmodes. The initial displacementis {mm and initial velocity is{mm/s. The displacement ofthe first degree of freedom inmm at time t=3 s is0.3141O 0.56860.15330.1543

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Answered: A two degree of freedom undamped system…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Given the vibrating system below: K4 Y(t) =Ysin30t where for = 30 and Y=20mm Find the following K1 K2 m C3 H C2 C1 C5 C4 1. Frequency Ratio 2. Displacement Transmissibility Ratio 3. Absolute displacement of the mass 4. Type of Damping 5. Equation of motion x(t). Assume Initial conditions for displacement and velocity 6. Graph 2 cycles of the vibrating system. You can use third party app for this. M = 10 kg K1=100 N/m K2= 80 N/m K3=75 N/m K4= 120 N/m C1 = 20Ns/m C2=40 Ns/m C3= 35Ns/m C4= 15 Ns/m C5= 10 Ns/m
2. The equation of motion for a damped multidegree of freedom system is given by Where [m] = [m]{x} + [c]{x} + [k]{x} = {f} [100 = 0 0 0 10 0 10. 1000-4 {f} [c] 8 –4 0 8 – 4 -4 4 0 8 4 = 100 2 0 = Focos(wt) -2 -2 The value of Fo 50N and w 50 rad/sec. Assuming the initial conditions to be zero and using the modal coordinate approach, find out the steady state solution of the system in the modal coordinate for first mode. Plot the steady state solution using the computational tools. 0 −2], [k] = = 2
1 Free Vibration Response of Single Degree of Freedom System(100 %) Figure 1 represent a simple vibration system. The free vibration response of an undamped single degree of freedom (SDOF) oscillator is given by its displacement x(t) satisfying x(t) = x(0)sin*(wt)e-2dwt + v(0) (1) -cos(wt)e-10dwt %3D where t is time in seconds and w = Vis the natural frequency of the system with m and k being the mass and the stiffness of the system. d is the damping coefficient of the system. Define v(t) and a(t) as the time dependent velocity and acceleration of the system. Write an M-file script using functions that will compute and plot 1. The displacement of the system x(t) over time 2. The velocity of the system v(t) over time 3. The acceleration of the system a(t) over time for three damping coefficients (d = 0,1,5) within a time interval 0 < t < 10 s. You will need THREE(3) functions, one for each displacement, velocity and acceleration calculations. Assume m = 10, k = 1 and that r(0) = v(0) =…
The following is the equation of motion for forced damped vibration of a mass-damper system: mx + cx + kx Fo sin wt The magnification factor variation with respect to the frequency ratio is given in Figure Q5 for various damping ratio values. If it is known that for the system examined the damping ratio is 0.3 and the magnification factor takes the value 0.8, then how the vibration amplitude can be further reduced by only altering the mass, damping coefficient and stiffness coefficient? 4/1055 Amplitude ratio: M = 2.8 2.4 2.0 1.6 1.2 1.0 0.8 0.4 0 = 5.0 0.4 = 0.1 = 0.3 X = 0.4 -=0.5.-- = 1.5 = 2.0 0.8 1.2 1.6 2.0 1.0 Frequency ratio: r = = 3.0 2.4 2.8 3.2 W Wn
An experiment was carried out on a SDOF system to estimate the natural frequency and damping. The time history plotted below has the response in centimetres and the time in seconds, as shown in Figure Q10 below. Estimate values for the following and choose the nearest values from the list given below: the damped natural frequency in Hz; the damping ratio using the logarithmic decrement method; and the natural frequency in rad/s. Ju(t) 2.00 AMA 1.00 0.00 0.00 Figure Q10 0.80 1.60 Select one or more: O a. 4.92 b. 0.781 c. 0.625 O d. 0.330 O e. 0.052 2.40 3.20 4.00 t
The block diagram given below; A) Reduce it B) G1(s)=2/s ; G2(s)=1/4s+2 ; G3(s)=4 ;H(s)=0.5 Given the values of the system; find the time constant, its natural frequency and damping rate and explain what kind of dynamic behavior it exhibits accordingly. C)Find the poles and zeros of the system according to the values in (B).Is the system stable? Find the unit step response (Inverse Laplace).
1. Linearized the dynamic model of the system shown below: - cô – mgL sin 0 + u. daor at| L sine mg
Q5. For a point at distance 50 m and angle 450 to the axis which of the following statements are correct? Consider an infinite baffled piston of radius 5 cm driven at 2 kHz in air with velocity 10 m/s. You may choose multiple options. a. The constant term is given by 515.03 b. The distance dependent term is given by e-jk50/50 c. The directivity term is given by j1(Ka sin 450)/sin 450 d. There is no time dependent term.
For the system shown in Figure 2, u (t) and y (t) denote the absolute displacements of Building A and Building B, respectively. The two buildings are connected using a linear viscous damper with damping coefficient c. Due to construction activity, the floor mass of Building B was estimated that vibrates with harmonic displacement that is described by the following function: y(t) = y,cos (wt). k/2 Building A H k/2 M(t) C 73(1) Building B Equivalent (Building A) 00000000 Figure 2: Single-degree-of-freedom system in Problem 2. 111 uft) Please compute the following related to Building A: (a) Derive the equation of motion of the mass m. (b) Find the expression of the amplitude of the steady-state displacement of the mass m. (1) (Building B)
The response of a system 1s given by x(t) = 0.003 Cos Böt +0.0045in 30t m. Defermine the amplitude Og motion, the frequency in Hz, the frequency in rad/s, the frequency n rpm, the phase angle and the responce in the form of x(t)= Asn(wk tp) og mction, the period
The damped frequency of oscillation of an open loop underdamped system = 12rad/sec The magnitude of the real part of the underdamped system = 16 Determine the natural frequency (Answer to 0 decimal places)
O choose 1/2 dynamics model or whole- car dynamic model of the automobile O obtaion the motion differential equations of the chosen model and the equations of non-damping free vibration O calculate the natural frequencies and natural modes by Matlab program 1/2 dynamic model of the automobile parameters O% body mass M 690kg O mass moment of inertia J, = 1222kgm O wheel mass M= 40.5kg. M= 45.4kg O tire stiffness k =k, - 192000N/m O sispension stiffness ky 17000N/m. k, =2000ONim O suspension damping coefficient c c, = 1500Ns/m O geometry dimensions a= 1.25m, b= 1.51m whole-car dynamic model of the automobile Xe kater el kel lee kal te parameters O body mass m,-1380kg O mass moment of inertia of pitch 1,-2444kgm O mass moment of inertia of roll 1,-3800kgm O Viwheel distance t-0.74m O the other parameters are the same as the l/2 dynamic model

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