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Topics | Benefits |
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Torsional vibrations | Confidentiality |

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**Q1:**For the following system, a) obtain the equivalent system b) derive the equation of motion using Energy Method, where, KE=½ m x², and PE=½ k x², c) find the natural frequency.See Answer**Q2:**A slender rod of length l and mass m2 is attached by a frictionless pivot at 'A' to a block of mass m1. The blockmoves horizontally on rollers. The position of the block is described by the x coordinate and bar rotationalposition by 0:See Answer**Q3:**In the following Figure a system consists of a block with mass m, spring K and a damper C; is attached to the floor where the block has a vertical oscillation x(t), and floor is vibrating vertically y(t) at 30 Hz. 1) For the case which system damping ratio is zero, what should be the natural frequency of the block vibration in order to reduce the relative motion of the block to floor by 12 dB. [2 marks] 2) If we consider a value for damper; C, which makes it equal to 10% of critical damping then what would beX/Y) ratio in this case. [1 marks] 3) Explain and justify whether adding more damping can reduce the vibration of the block in response to floor vibrating at 30 Hz [2 marks] See Answer**Q4:**THREE SPRINGS 2 A MASS ARE ATTACHED TO A RIGID WEIGHTLESS BAR AB FIND THE NATURAL FREQ OF THE SYSTEM See Answer**Q5:**For he 1-0OF sywanm auojaot to a ulangular ariodio fording funation (node ed by a FourlerSee Answer**Q6:**(Forced Vibration)Determine the amplitude of the steady state displacement of the mass for forced vibration. See Answer**Q7:**A fragile instrument and its housing, which together weigh 10 lbs, are mounted on four symmetrically located identical springs as a means of isolating the instrument from the vibration of the table supporting it. Measurements indicate that the table reaches a maximum amplitude of 0.004 inch somewhere in the frequency range of 20 to 30 Hz.Determine the spring constant k of each spring so that the amplitude of vibration of the instrument will be limited to 0.0002 inch as a maximum.See Answer**Q8:**A sensitive computer is being transported by rail in a box car. Acelerometer measurements indicate that when the train is traveling at its normal speed of 85 m/s the dominant component of the box car's vertical acceleration is 8.5 m/s² at a frequency of 5.73 Hz. The crate in which the computer is being transported is being tied to the floor of the boxcar. What is the required stiffness of the isolator with a damping ratio of 0.5 such that the acceleration amplitude of the60 kg computer is less than 0.5 m/s2? With this isolator, what is the displacement of the computer relative to the crate?See Answer**Q9:**A steel frame supports a turbine -driven exhaust fan. At a speed of 400 rpm, the amplitude of motion is 4.5 mm measured at the floor level of the fan. At a speed of 500 rpm, the amplitude is 10 mm. No resonant condition is observed in changing speed from 400 to 500rpm. To decrease this intolerable vibration, it is proposed to add a slab of concrete beneath the turbine. The mass of the slab is chosen such that the total mass of the system with the fan is doubled. Does this solve the vibration problem?See Answer**Q10:**During an earthquake, the one-story frame structure shown below is subjected to a ground vibration amplitude of 0.1 m at 10 Hz. a) Determine the amplitude of motion of the girder.Assume the girder is rigid and the structure has a damping ratio of 0.03. b) What is the amplitude of acceleration of the structure? See Answer**Q11:**A pump system is to be installed as shown in the diagram below. The pump and the basehave a combined mass of 150 kg. The pump operates at 1750 rpm with a maximum unbalance of 0.002 kg-m. The isolation system has an equivalent stiffness of 7.3 x 106 N/m,and a damping ratio of 0.1. Determine: a) The steady state displacement amplitude of the pump b) The force transmissibility ratio c) The force transmitted to the ground d) Should the physical damping of the isolation be decreased or increased to reduce the force transmitted to the base at the operating speed? See Answer**Q12:**FIND THE NATURAL FREQ.Of THE SYSTEM SHOWN.NOTE:SHOWN IS THE STATIC EQUILIBRIUM POSITION.See Answer**Q13:**A SYSTEM HAS THE FOLLOWING CHARACTERISTICS: m =10 kg k=4000N/m 3=10% Xozc, *.=0 A forcing function F(t) = 200 t sin (10t) is applied DETERMINE THE xp (t) for the systemSee Answer**Q14:**A system with a w= 20lb k=500lb/m = 0.15 and zero initial conditions is subjected to the forcing function shown below EVALUATE THE DISPLACEMENT @ t= 315See Answer**Q15:**IN CLASS , WE DERIVED THAT THE FORCE TRANSMITTED(LECTURE O7/30/2018)IS GIVEN BY \frac{F_{T}}{F_{0}}=\frac{\sqrt{1+(23 r)^{2}}}{\sqrt{\left(1-r^{2}\right)^{2}+(2 q r)^{2}}} DETERMINE THE VALUE E OF THAT WILL RENDER F tmax for A specific 3SPECIFIC S.MASee Answer**Q16:**m=10kg k=4000n/m c=400n-s/m r= 0.1 m F(t) = 300 sin (20t) EVALUATE THE STEADY STATE RESPONSE Oss(t)See Answer**Q17:**3. Find the particular solution for the system shown in Fig. 1for the input = F sinot See Answer**Q18:**For the system shown below, determine the amplitude of the steady state displacement of point A for forced vibration. See Answer**Q19:**Problem 1. Simulate the unit step response of the dynamic system given by G(s)=\frac{1}{\tau s+1} when T = 1 using MATLAB or OCTAVE. Compare it with the analytical solution of HW02Problem 4. Provide your code and plot.See Answer**Q20:**A steel shaft of diameter d and length I is fixed at one end and carries a propeller of mass m and aradius of gyration of r, at the other end (see Figure 1). Data: d = 5 cm,l=1m, m = 100 kg, r, = 10 cm 1- Determine the fundamental natural frequeney of vibration of the shaft in axial vibration Determine the fundamental natural frequency of vibration of the shaft in torsional Task 1.3- Is it possible to change the system parameters (d, l, m, r,) such that the fundamentalfrequencies for both axial and torsional vibration become identical?[30%] If yes, what are the new parameter values? Explain the method and report your detailedanalysis leading to the new values. If no, explain in detail why it is impossible. I.Note 1: In Tasks 1.1 and 1.2, derive boundary conditions, start from the relevant equation of motionand apply the boundary conditions, find characteristic equation, solve it for natural frequencies, andfind the fundamental frequency.See Answer

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