Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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- A force of 20 newton stretches a spring 1 meter. A 5 kg mass is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 10 times the instantaneous velocity. 1) Let x denote the downward displacement of the mass from its equilibrium position. [Note that x>0 when the mass is below the equilibrium position. ] Assume the mass is initially released from rest from a point 3 meters above the equilibrium position. Write the differential equation and the initial conditions for the function x(t) 2) Solve the initial value problem that you wrote above. 3)Find the exact time at which the mass passes through the equilibrium position for the first time heading downward. (Do not approximate.) 4)Find the exact time at which the mass reaches the lowest position. The "lowest position" means the largest value of xarrow_forwardIn matlabarrow_forwardFind the values of rise time (tr), peak time(tp), settling time(ts) and maximum value from the following figurearrow_forward
- 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] = = 2arrow_forward1 Study the below response which obtained from HVACexperiment to find the following: Setpoint Upper Limit Lower Limit = Digital Scopes Chamber Temp 23.0 C Setpoint Ambient 21.4 22.5 C Temperature (C) MeasuredAV 23.5- Signal Generator 2 23.4- Signal Type 23.3- 23.2- 23.1- Amplitude 0.00 23- Frequency 0.0080 Hz 22.9- Offset 0.50 22.8- 22.7- Control Parameters 22.6- Vh amp 2.50 V 22.5- 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 Vh off 2.50 V ATh 0.25arrow_forwardThe mass, damping, and stiffness of the system m C can be adjusted to produce different dynamic responses. Match the frequency response functions (A)-(D) with their corresponding time-histories (W)-(Z). (W) (X) (A) (B) (Z) (D) (Y) A [Choose ] [ Choose ] [ Choose ] D [Choose ] B.arrow_forward
- 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 modelarrow_forwardibä 30 A vehicle wheel, tire, and suspension can be modeled as a SDOF spring and mass as depicted below: The mass of the wheel and tire is measured to be 300 kg and its frequency of oscillation is observed to be 10 rad/sec. What is the stiffness of the wheel assembly? Also, calculate the frequency in Hz * ?and the time of period in sec اكتب المطلوب من السؤال فقط بدون ذکر التفاصيل )النواتج المطلوبة فقط(. 30 درجة vchicle frame -suspension tire and wheelarrow_forward1 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…arrow_forward
- A test was undertaken to find the dynamic properties of a SDOF system. The measured transient response recorded is shown in Figure QA2a. If the stiffness of the system is 1,000 N/m estimate: i) the damping ratio, ii) the undamped natural frequency, and iii) the mass of the system. Displacement (m) 0.08 0.06 0.04 0.02 O -0.02 -0.04 -0.06 -0.08 Figure QA2a 0.5 Time (s) 1.5 2arrow_forwardMatlabarrow_forward2- 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.2arrow_forward
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