How many degrees of freedom are required to model the systems shown in figures (A to D)? Also,a set of generalized coordinates which can be used to analyze the systems' vibrations if thesystems undergo planer motion.massless linkagecarriage3K$2Kroller3K2m4mmNo slippingmassless &friction lesspufley3水mAll pulleys ore mosslesand frictionless2KFig (B):-Fg (A):-lo slipping2K 3KRollercarrioge4mAll pulleys ere masslesand frictionless2KFig (D):-(C):-

First we will evaluate the variables involved in system and then we will figure out number of…

systems undergo planer motion. massless linkage corriage 3K roller 3K m 2m 4m m r massless f friction less pulley No slipping 3k All pulleys are mossles and frictionless 2K Fig (B):- Fg (A):- lo slipping 2K 3K Roller carrioge 4m All pulleys ere massles and frictionless 2K Fig (D):-

systems undergo planer motion. massless linkage corriage 3K roller 3K m 2m 4m m r massless f friction less pulley No slipping 3k All pulleys are mossles and frictionless 2K Fig (B):- Fg (A):- lo slipping 2K 3K Roller carrioge 4m All pulleys ere massles and frictionless 2K Fig (D):-

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

MECHANICAL VIBRATIONS USE VIRTUAL WORK HOW DID IT REACH TO THIS ANSWER? THIS IS ACCORDING TO THE ANSWER KEY OF THE BOOK The uniform bar shown in Fig. P3.6 has mass m, length l, and mass momentof inertia I about its mass center. The bar is supported by two springs k1and k2, as shown in the figure. Obtain the differential equation of motion anddetermine the natural frequency of the system in the case of small oscillations.
Determine the mathematical model for the translational-rotational dynamic system shown in the figure. Note that: • f(t) is a force input • at the pivot, there is a torsional damper, bT • The pendulum’s rod (l 1 +l 2 +l 3 ) can be assumed to be massless. Make sure to show all your steps, sign conventions, ?1(?) and ?(?) orientations, assumptions, diagrams, etc.
A Jello desert resting on a plate is starts wiggling when it is sheared to the side 0.5 cm as is set on the table. The desert is a rectangular prism with a square face 25.0-cm on a side and a height of 12.0 cm. A quick Google search reveals that the density of Jello is 1140 kg/m3 with shear modulus of 530 N/m2. What is its rate of oscillation? If the energy of oscillation is dissipated at the rate of 5.00 x 10-5 J per second how long will the block wiggle?
A box that contains of a 250 kg fragile instrument is transported by a truck that is subjected to a vertical harmonic motion given by ?(?) = 0.02 sin 3?. Assume that the instrument only moves in vertical translation and is supported by four springs with stiffness, k = 500N/m as simplified in Figure Determine the maximum displacement, velocity and acceleration experienced by the instrument
A washing machine has 60 kg mass, and 15 cm tub radius. Machine dries the unbalanced3 kg laundry by rotating with 1000 rpm.a) What would be the dynamic force transmitted to the foundation if there is no vibrationisolation for the machine?b) An isolation with damping ratio 0.1 is applied to the machine. In this case, if thetransmitted force is decreased by 90 % what would be the natural frequency of the machine?c) In this case, what would be the vibration amplitude of the machine?
In the system in the figure, the static equilibrium position of the thin, slender homogeneous rod of mass m and length L is horizontal.During the movement of the system, the bar is separated from the horizontal by small angles. (A makes oscillating motion with small angles relative to the simple support point)a) Find the equation of motion of the system in terms of the given parameters.b) Since M=4 kg, m=1 kg, L=1 m, k=600 N/m, c=200 Ns/m, F=300 N, w=4 rad/s, is there resonance in the system? If there is resonance, what would you recommend to get rid of resonance?
1. A .6kg block is hung from a spring with a force constant of 25 N/m. Calculate the displacement of the spring from its equilibrium length, assuming it is hung vertically and neglecting the spring mass. 2. The mass in (1.) is pulled downward by an additional 6 cm and held steady. Calculate the potential energy input corresponding to this additional displacement. 3. Calculate the period of oscillation of the mass/spring system once the object is released. 4. Write an expression for the vertical motion of the system, along the y (vertical) axis, in the form: ?(?) = ? cos(?t) (Use the appropriate values of A and ω in your expression). 5. Calculate the maximum speed of the oscillating object and its maximum kinetic energy. Do your results make sense based off what you got in 2? (I posted all 5 parts but could you answer only 4 and 5? Thank you!)
Let’s look at a simplified model of a car that’s dropped onto the ground. Model the suspension as a single linear spring and the rest of the vehicle as a single lumped mass. The car is dropped from a height of h1 = 0.9m. What is the maximum mass m for which the suspension does not bottom out? Assume a maximal allowable suspension travel of 10 cm and a spring constant of k = 2.4x10^6 N/m.
A washing machine with a mass of 60 kg and a drum radius of 15 cm, rotates at 1000 rpm and washes 3 kg of unbalanced laundry. a) How much dynamic force would be transmitted to the ground if no vibration isolation was taken from the machine?b) What would be the stiffness (k) of the visco-elastic floor if an insulation measure with a damping ratio of 0.1 was taken, which would reduce the force transmitted to the floor by 90%?
Consider the mechanical system of this figure comprising two wheels of mass m, inertia j, andthree springs each of stiffness k. The wheels move on two fixed horizontal surfaces during thesystem's free vibrations. Derive the mathematical model of this mechanical system.
A 0.1 kg object oscillates as a simple harmonic motion along the x-axis with a frequency f = 3.185 Hz. At a position x1, the object has a kinetic energy of 0.7 J and a potential energy 0.3 J. What tge amplitude of oscillation
The structure shown in figure has a mass of 100 kg and a translational stiffness of 40,000 N/m. It is excited by a harmonic force having an amplitude Po = 500 N and an excitation frequency ω = 15 rad/s. The damping factor for the structure is ξ = 0.1. The initial conditions are u(0) = 6 cm and ώ(0) = 0. For the steady-state vibration determine: (a) The amplitude of the stady-state displacement. (b) Its phase with respect to the exciting force. (c) The maximum velocity and acceleration of the response. (d) Determine the equation that describes the total displaement of the structure as a function of time.