For a two degree of freedom system subject to free undamped vibrations, the inertia and stiffness coefficient matrices are given by: and [k] = [400 67500] [M] = [1000 2.5 8101 2.5 a) What type of coupling exits in this system? Briefly explain why. b) Calculate the natural frequencies of the system. c) Calcuate the ratio of amplitudes at each natural frequency.

For a two degree of freedom system subject to free undamped vibrations, the inertia and stiffness coefficient matrices are given by: and [k] = [400 67500] [M] = [1000 2.5 8101 2.5 a) What type of coupling exits in this system? Briefly explain why. b) Calculate the natural frequencies of the system. c) Calcuate the ratio of amplitudes at each natural frequency.

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

See similar textbooks

Similar questions

Let e be the counterclockwise angular displacement of the disk in the following system. a) Derive the governing differential equation of the system by using the Newton 2d law. b) Find the natural frequency of the system c) For what value of c is the damping ratio of the system equal to 1.15? fy-10 cm f30 cm m2 m1 Jputey10 kg-m m;-10 kg my-25 kg k-1x10' N/m
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.
1) Guess the form and solve for the particular solution of a driven oscillator described by the equation: mx" + cx' + kx = Fosin(wt) 2) A mass of 4 kg on a spring with k = 4 N/m and a damping constant c = 1Ns/m is driven by a force following the function Focos(at); where FO = 2 N. Find the driving frequency that causes practical resonance and find the amplitude. 3) Suppose there is no damping in a mass and spring system with m = 5, k = 20, and Fo= 5. Suppose is chosen to be precisely the resonance frequency. a) Find a b) Find the amplitude of the oscillations at time = 100, given that the system is at rest at / = 0.
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).
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
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.
The equation of motion of a simplified model mechanical system is given below. of a m, o X₁ ki+k₂ k₂ O +1 NA 1/2 FU 10 ma -k₂ k₂ | k₂ = 10,000 N m₁ = 40 kg / m₂ = 130 kg, k₁ = 20,000~ m 0 a) Natural Freequency b) Find the mass normalized mode shapes of the system. c) Drave the mass normalized mode shapes.
xa 0- 1 point) Which of the systems presented on Fig. 2 is stable and which unstable? (a) t Fig. 2. System response (b) A
Get the equation of motion by drawing the free body diagram of the given systems. a) Get the system's transfer function and find the unit digit answer. Show all decals in detail. m = 1 kg b= 20 Ns/m k = 125 N/m F ww k b) get the transfer function of the system. X(s)/Pg(s) =? Show all decals in detail. resistance R k Pg massless piston area (A) capacitance
The figure shows a vibratory system with two degrees of freedom; the OA bar is rigid and homogeneous of mass m = 6 kg and length l = 2 m.Suppose that:c1 = 200 kN s/mc2 = 600 kN s/mk1 = 500 N/mk2 = 300 N/m a) Determine the equations of motion of the system. b) Determine the matrices associated with the vibratory system. c) Determine the natural frequencies.
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
A spring-mass-damper system consists of a mass m=120 slug, a spring constant k = 40 lb/in, and a damping coefficient c = 5lb*sec/in. Find the following: a.) Natural frequency b.) The damping ratio c.) Damped frequency. d.) Assume the initial conditions to be Uo = 0.2in, Vo = 0.5 in/sec, find the maximum deflection and plot the response, u(t).