3) A certain machine of mass 400 kg has a shaft that rotates at 1800 rpm. It is known that the machine shows resonance at 1200 rpm. An absorber is to be mounted on top of the machine so that the amplitude of its vibration response with the absorber mounted, within the range 1000-2000 rpm, is less than 50 % of its static response measured without the absorber. Here, by static response, we mean the response if the magnitude of the dynamic force were applied statically. Design the absorber. That is find suitable values of absorber mass and stiffness. Hint: Firstly, aim to reduce the amplitude at one frequency, then check the situation at the other frequency. Do this until you find a solution. If you do not think that there is a solution, state it with an acceptable arguments.

3) A certain machine of mass 400 kg has a shaft that rotates at 1800 rpm. It is known that the machine shows resonance at 1200 rpm. An absorber is to be mounted on top of the machine so that the amplitude of its vibration response with the absorber mounted, within the range 1000-2000 rpm, is less than 50 % of its static response measured without the absorber. Here, by static response, we mean the response if the magnitude of the dynamic force were applied statically. Design the absorber. That is find suitable values of absorber mass and stiffness. Hint: Firstly, aim to reduce the amplitude at one frequency, then check the situation at the other frequency. Do this until you find a solution. If you do not think that there is a solution, state it with an acceptable arguments.

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

The mechanical behavior of a biological tissue can be modeled as Maxwell body. The tissue is subject to the force profile: F(t) = F,(1-e) for 120 where t is time, a is a rate constant and equal to 0.5/s, and F,= 1 nN. Determine the value of the spring constant (k) if damping coefficient u = 4•104kg/s, and deformation at t = 2s is 8.16 μm.
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
A two degree of freedom undamped system has natural frequencies 2 rad/s and 3 rad/s and corresponding mode shapes {{{ and . A damping ratio of 2% is assumed for both modes. The initial displacement is {mm and initial velocity is {mm/s. The displacement of the first degree of freedom in mm at time t=3 s is 0.3141 O 0.5686 0.1533 0.1543
2. A spring with k = 4500 N/cm supports a mass of 1.5 Kg. Determine the 'natural frequency' of this system in rad/sec & Hz? 3. Determine the fourier series that represents the function as
(a)A 0.5 kg mass is attached to a linear spring of stiffness 0.1 N/m. Determine the natural frequency of the system in hertz. b) Repeat this calculation for a mass of 50 kg and a stiffness of 10 N/m. Compare your result to that of part a.
2- I need answer of all sub-parts questions. Thanks The figure shows a simple model of a motor vehicle that can vibrate in the vertical direction while traveling over a rough road. The road surface varies sinusoidally with an amplitude of 0.01 m and a wavelength of 6 m. The vehicle has a mass of 1007 kg. The suspension system has a total spring constant of 40 kN/m and a damping coefficient of 20 kN.s/m. The vehicle average speed is v = 100 km/hr. The objective is to determine the vehicle steady-state displacement amplitude as well as the respective transmitted force. Calculate the resultant frequency ratio of the above model. Calculate the steady state amplitude of the vehicle. Determine the force amplitude that will be felt in the vehicle at the steady-state due to the bumpiness of the road.
4. A convenient way to measure damping in a single-degree-of-freedom system is called logarith- mic decrement of free response. Consider the free response given by (4). Let's denote t₁ and t2 denote the times corresponding to two consecutive displacements ₁ and 2 measured one cycle apart, i.e., where t₂ = t₁ + T 2π Wd According to (4), show that the logarithmic decrement dis T = x1 8 = log = x2 where log has base e. Combine (5), (7), and (8) to obtain = (WnT 8 4π² +8² Will this method work for other initial conditions? why?
Question 1: A pressure gauge which can be modeled as a Linear Time-Invariant (LTI) system has a time response to a unit impulse input h(t) given by (Ge-2t +e-«") u(t). For a certain unknown input, the output y(t) is observed to be (4e7t – 8e2")u(t). For this observed measurement, derive the true pressure input x(t) to the gauge as a function of time. Assume that the input signal is right-sided.
In this Problem, the system of Fig. 5.4.14 (Attached) is taken as a model for an undamped car with the given parameters in fps units. (a) Find the two natural frequencies of oscillation (in hertz). (b) Assume that this car is driven along a sinusoidal washboard surface with a wavelength of 40 ft. Find thetwo critical speeds. m = 100, I =800, L1 = L2 = 5, k1 =1000, k2 = 2000
If a mass of 6 kg oscillates on a spring having a mass 3 kg and stiffness 11200 N/m, then the natural frequency of the system in rad/sec will be
sum - 1 : determine magnification factor of forced vibration produced by oscillator fixed at middle of the beam at a speed of 600 rpm. The weight concentrated at the middle of the beam is 5000 N and produces statically deflection of the beam equal to 0.025 cm. Neglect the weight of the beam and damping is proportional to velocity of 2.5 cm/sec and force = 500 N sum - 2 : An automobile whose weight is 150 N and it is mounted on 4 identical springs due to its weight it sags by 250 mm . each shock absorber has damping coefficient of 0.4 N for a velocity oof 30 mm/sec. The car is placed on a platform which moves vertically at resonance speed having an amplitude of 10mm. Find the amplitude of the car Sum - 3: A SDOF has undamped natural frequency of 7 rad/sec. and a damping factor of 10%. The initial conditions are x0 = 0 and V0 = 0.5 m/sec. Find damped frequency and equation of motion of the system Sum- 4; A SDOF system with a mass 25 kg and stiffness 10 N/mm with damping 0.15 Ns/m…
A 35 K G block is connected to a support through a spring (k=1.4 * 10^6 N/m) and a damper (c=1.8 * 10^3). The support is given a harmonic displacement of 10 mm at a frequency of 35 Hz. What is the steady state amplitude of the block?