A test was undertaken to find the dynamic properties of a SDOF system. Themeasured transient response recorded is shown in Figure QA2a. If thestiffness of the system is 1,000 N/m estimate:i) the damping ratio,ii) the undamped natural frequency, andiii) the mass of the system.Displacement (m)0.080.060.040.02O-0.02-0.04-0.06-0.08Figure QA2a0.5Time (s)1.52

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Answered: A test was undertaken to find the…

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
1 Problem You are given the following data (below) showing the steady-state output response, x(t), of a mass-spring-damper (stable, LTI) system to a sinusoidal input u(t) = A sin(wt). This snapshot is the response after all the transients have decayed (the time is shifted to start at zero for conve- nience). x 0.5225 Displacement pu(t) Sinusoidal force input x 0.1041 1.5 1 Y2 х 0.2783 Y1.372 0.5 h ok -0.5- -1 -1.5 x(t) M Assume: bl u(t) x(t) Horizontal Plane (no gravity) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time (sec) www k Using only the data provided above (the blue line is the input u(t) and the red line is the output x(t)), determine: 1. The frequency of the input in rad/s 2. The amplitude of the input, A 3. The frequency of the output in rad/s 4. The output-input ratio |G(iw)| = max(x(t)) max(u(t))' at the particular input frequency shown. 5. The phase (also called phase lag) of the output, $, at the particular input frequency shown in degrees. Note the phase is generally…
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
Given the vibrating system below: K1 K3 K4 Find the following 1. Keq 2. Ceq 3. Natural angular velocity K2 m C1 C3 C5 C2 C4 4. Damped angular velocity 5. Type of Damping 6. Equation of motion x(t). Assume Initial conditions for displacement and velocity Graph 2 cycles of the vibrating system. You can use third party app for this. 7. 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- Using Matlab, what are the step response curves of the closed-loop system, as shown in fig.1. the feedback represents the second-order dynamic system. (fill in the following table) For=0.4 Wn 1 3 6 9 10 R(S) 0.1 0.3 0.6 0.9 1 For w 5 rad/sec 3 Settling time Peak response 2 Wn s(s+23wn) Settling time Peak response C(s) Discuss the follow Which parameters or w occur on the rise time of the response? Which parameter increases the speed of response? Which parameters can be decreases the response amplitude? Which parameter decreases the steady error state? fig.2
Question 4 a) A control engineer has modelled the suspension system of a new model car using a 2nd order differential equation. Using Laplace Transform, the engineer has managed to work out the transfer function, which is given below: 0.001 s2 + 12s+81 What is the natural frequency, the damping ratio and the constant K of the system? Please show all calculations. b) The same engineer has studied the suspension system of a SUV vehicle and modelled it using again a 2nd order differential equation, which has resulted into the following 2nd order transfer function: Y(s) 32 U(s) 4s² +8s + 16 For this system first calculate the damping ratio and its natural frequency and state whether the system is underdamped, overdamped or critically damped. Then calculate the peak time, peak value, settling time and damped natural frequency of the system.
1. Verify Eqs. 1 through 5. Figure 1: mass spring damper In class, we have studied mechanical systems of this type. Here, the main results of our in-class analysis are reviewed. The dynamic behavior of this system is deter- mined from the linear second-order ordinary differential equation: where (1) where r(t) is the displacement of the mass, m is the mass, b is the damping coefficient, and k is the spring stiffness. Equations like Eq. 1 are often written in the "standard form" ď²x dt2 r(t) = = tan-1 d²r dt2 m. M +25wn +wn²x = 0 (2) The variable wn is the natural frequency of the system and is the damping ratio. If the system is underdamped, i.e. < < 1, and it has initial conditions (0) = zot-o = 0, then the solution to Eq. 2 is given by: IO √1 x(1) T₁ = +b+kr = 0 dt 2π dr. dt ل لها -(wat sin (wat +) and is the damped natural frequency. In Figure 2, the normalized plot of the response of this system reveals some useful information. Note that the amount of time Ta between peaks is…
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
1 Problem 5 4 State, x(t) SAWNO-Nw. ● ● Case 1 O 2 6 Time, sec. underdamped critically damped State, x(t) • overdamped 54321 ONS TY Case 2 2 ▷ Time, sec. 8 10 State, x(t) 5 2 + 3 4 Case 3 2 ▷ 6 Time, sec. 5432 State, x(t) & A & No. 2 Match each of the resposes above to one of the following second-order system types: • undamped Case 4 ▷ Time, sec.
:) Determine the equivalent mass of the system shown in Figure Q.A3c. X m 2r m Figure Q.A3c. m WE For the system shown in Figure QA1a write appropriate response variables and find the degrees of freedom. r= 10 cm /= 1.5 kg-m² m = 10 kg nollos 2k
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
1) Consider the baseband pulse x(1) = n(2) = 11 a) Derive the complex ambiguity function for x(t) and compare your result with the one obtained in class. b) Use MATLAB to compute the complex ambiguity function and compare it to part (a). c) Now, consider the pulse x(t) = sinc(Bt) i) Derive the complex ambiguity function for x(t) and compare to the ambiguity function of the rect pulse. Make your observations. ii) Plot the ambiguity function using the mesh function and using the contour function. iii) Use MATLAB to compute the complex ambiguity function and compare it to part (ii).

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