A 2.3-kg object is suspended using two linear springs (k1 = 45 N/m and k2 = 21 N/m), as shownbelow. Due to aerodynamic effects and other losses, you observe that the amplitude of the vibrationis halved after 5 complete cycles. If the initial mass was displaced 270 millimetres below theequilibrium position (i.e. negative initial displacement) and then released from rest, determine theposition of the mass after 11 seconds. Give your answer in millimetres rounded to one decimal place.Enter positive values if the mass is above the equilibrium position and negative values if it is belowthe equilibrium position.kk

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Answered: A 2.3-kg object is suspended using two…

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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In the system shown,m= 2 kg, k= 1000 N/m, theta= 30 degrees and the friction coefficient between the block and the surface is u. (a) If the block is displaced from equilibrium and released, the decrease in amplitude per cycle is 2 mm. Determine the coefficient of friction u. (b) If the initial displacement is 5 cm from equilibrium, determine the time and position when the block comes to rest.
A mass of 21.5 kg is vibrating freely at the end of 3 springs connected in parallel. The spring constants are 112.2 N/m, 412.8 N/m and 1051.5 N/m. Determine the frequency in Hz of the vibration. (Express answers to 2dp) Answer:
A set of scales consists of an instrumented spring from which the mass of the measured object can be deduced, and a damper to reduce oscillations of the readings. The mass of the scales is small and the damper is chosen to give critical damping when a 10-kg object is weighed. If a mass of 20 kg is placed on the scales, what is the damping ratio and how many cycles of vibration will occur before the reading on the scales settles to within 1% of the correct value?
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A mass-spring system of mass m = 0.2 kg and elastic constant k = 5 N/m is immersed in a viscous fluid which exerts a damping force on the system. Furthermore, the system is subjected to a harmonic forcing of intensity F_0 = 10 N and frequency w rad/s. The value of the damping constant is b = 1.5 Ns/m. If the system starts at rest and in its equilibrium position, find: a) the frequency w for which the system is in resonance; b) Make a graph of position v/s time where the amplitude and period of the system can be seen explicitly if the frequency w is equal to twice the resonance frequency; c) Make a graph of amplitude v/s frequency where the maximum frequency and the resonance frequency of the system can be seen explicitly.
Assume that you are examining the characteristics of a suspension system of a 2000 kg automobile. The suspension "sags" 10 cm when the weight of the entire automobile is placed on it. In addition, the amplitude of the oscillation decreases by 50% during one complete oscillation. Estimate the values of k and for the spring and shock absorber system of each wheel. Assume each wheel supports 500 kg.
An undamped simple harmonic oscillator has mass 2.0 kg and spring constant 50 N/m. The initial displacement from equilibrium (at time t = 0) is 0.30 m and the initial velocity is 2.0 m/s. 2. From the initial conditions, determine the energy of the oscillator. Next, use the value of the energy to determine both the displacement and velocity amplitudes. Determine and display the displacement in the form x(t) = Ccos(@ot + q), where C is in meters and o is in radians.
Two identical springs of free length L0 and stiffness k are attached tothe collar of weight W. Friction between the collar and the horizontal rod maybe neglected. Assuming small amplitudes, (a) derive the differential equation ofmotion; and (b) find the frequency given that W =1N, L0 =0.1m, b=0.15 m,and k = 80 N/m.
A single cylinder engine can be treated as a rotating unbalance model where the mass of the piston, m, acts at an eccentric distance, e which is half of the stroke. Determine the displacement amplitude of the engine in millimetres when it is rotating at a speed of 344.4 rpm. The engine parameters are: Mass of engine, M = 447.8 kg; keq = 220.3 kN/m; ceq = 2843.2 Ns/m; m = 10.6 kg and Stroke (i.e. 2e) = 236 mm. Give your answer to 2 dp. Answer:
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