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MODEL QUESTION PAPER

Subject: Mechanical Vibration Branch: Mechanical Class: BE Semister: VIII

1) Harmonic motion is A) Necessarily a periodic motion B) An aperiodic motion C) A motion described in a circle D) A random motion Ans A 2) The velocity vector in a vector diagram for a harmonic motion A) Lags the displacement vector by 180° B) Leads the displacement vector by 90° C) Lags the displacement vector by 90° D) Leads the displacement vector by 180° Ans B 3) If harmonic motion of same frequency and same phase are superimposed in two perpendicular directions ( x and y) then, the resultant motion will be, A) circle B) An ellipse C) An square D) An rectangle Ans c 4) Beats phenomenon occurs when a vibrating system is subjected to two different frequencies which are A) Quite different B) Equal C) Slightly different D) Integral multiple of each other Ans C 5) The vector representing acceleration on a vector diagram for a harmonic motion A) Lags the displacement vector by 90° B) Lags the displacement vector by 180° C) Leads the displacement vector by 90° D) Leads the displacement vector by 180°

Ans C 6) Equivalent stiffness of spring connected in paralled having stiffness k1 and k2 can be given as A) K = k1+ k2 B) K = k1- k2 C) 1/k = 1/k1 + 1/k2 D) 1/k = 1/k1 - 1/k2 Ans A 7) If the amplitude of harmonic motion is large, its frequency A) Will always be high B) Will always be less C) Can have any value D) Will be zero Ans c 8) Body having simple harmonic motion is represented by A) x = A sin ωt B) x = A cos ωt C) x = - A sin ωt D) x = - A cos ωt Ans A 9) The natural frequency of torsional vibration is given by A) ωn = (-kt)/I B) ωn = kt/I C) ωn = √(kt/I) D) ωn = √(2&kt/I) Ans C

10) Resonance is a phenomenon when the frequency of external exciting force is A) Twice the natural frequency of the system B) Half the natural frequency of the system C) Same as the natural frequency of the system D) None of the above Ans c

11) Natural frequency of the system is due to A) Free vibration B) Forced vibration C) Resonance D) Damping Ans A

12) If the particle of a body vibrate along a circular arc, whose centre lies on the axis of the shaft then the body is said to have A) Transverse vibration B) Longitudinal vibration C) Torsional vibration D) None of the above Ans C 13) In the spring mass system if the mass of the system is doubled with spring stiffness halved, the natural frequency of longitudinal vibration A) Remained unchanged B) Is doubled C) Is halved D) Is quadruped ANS C 14) If the spring mass system with m and spring stiffness k is taken to very high altitude , the natural frequency of longitudinal vibrations A) Increases B) Decreases C) Remain unchanged D) May be increase or decrease depending upon the value of the mass And C 15) In a spring mass system of mass m and stiffness k, the end of the spring are securely fixed and mass is attached to intermediate point of spring. The natural frequency of longitudinal vibration of the system A) Is maximum when mass is attached to mid point of the spring B) Is minimum when mass is attached to mid point of the spring C) Decreases as the distance from the top end where mass is attached decreases D) Decreases as the distance from the bottom end where mass is attached decreases Ans B

16) Two springs have spring stiffness of 1500 N/m and 2000 N/m respectively. If they are connected in series, what is the spring stiffness if they are replaced by an equivalent system.3500 N/m

A) 3500 N/m B) 1166 N/m C) 857.63 N/m D) None of the above Ans C

17) Which type of vibrations are also known as transient vibrations? A) Undamped vibrations B) Damped vibrations C) Torsional vibrations D) Transverse vibrations Ans B 18) During transverse vibrations, shaft is subjected to which type of stresses? A) Tensile stresses B) Torsional shear stress C) Bending stresses D) All of the above Ans C

19) In which type of vibrations, amplitude of vibration goes on decreasing every cycle? A) Damped vibrations B) Undamped vibrations C) Both a. and b. D) None of the above Ans A

20) Which among the following is the fundamental equation of S.H.M.? A) x + (k / m) x =0 B) x + ω2x =0 C) x + (k/ m)2 x =0 D) x2 + ωx2 =0 Ans B

1) The units of viscous damping coefficient is A) N-m/sec B) m/N-sec C) N-sec/m D) N-m-sec Ans C 2) The effect of damping on the natural frequency of the system is to A) Reduce it considerably B) Increase it considerably C) Reduce it marginally D) Increase it marginally Ans C 3) A forced vibration system vibrates at A) Natural frequency of the system B) Frequency of external excitation C) Frequency of internal excitation D) None of the above Ans B 4) Damped natural frequency of a system with ωn =100 Hz and ς = 20% is given by A) 92 Hz B) 94 Hz C) 96 Hz D) 98 Hz Ans D 5) A rotary system has a damping coefficient of 40 N-m-sec/rad. The damping torque at a velocity of 2 rad/s, will be A) 20 N-m B) 40 N-m C) 80 N-m D) 100 N-m Ans C 6) In case of viscous damping the frequency of damped vibration is A) Equal to that of undamped vibrations B) Less than that of undamped vibrations C) Greater than that of undamped vibrations D) Independent than that of undamped vibrations Ans B 7) The response of a damped forced vibration system A) Leads the system excitation ( for all values of ω/ ωn) B) Lags the system excitation ( for all values of ω/ ωn) C) Leads the system excitation ( for all values of ω/ ωn > 1) Ans B 8) In the case of steady state forced vibration at a resonance, the amplitude of vibration is A) Inversely proportional to damping coefficient B) Inversely proportional to damping ratio C) Inversely proportional to resonant frequency D) Directly proportional to resonant frequency Ans B 9) The equivalent viscous damping coefficient Ceq for coulomb damping is given by A) 4F/πωx B) 4πF/ωx C) πωx/4F D) ωx/4Πf Ans A 10) If ωmax is the frequency at which the peak amplitude occurs and ωn is the natural frequency of the system then In a forced vibration system with damping, the higher the damping, A) More will be the difference between ωn and ωmax B) Less will be the difference between ωn and ωmax C) The difference of ωn and ωmax is independent of damping in this system D) The difference between ωn and ωmax will be zero Ans A 11) If frequency of excitation of a forced vibration system with negligible damping is very close to natural frequency of the system, then the system will A) Execute harmonic motion of large amplitude B) Beat with a very high peak amplitude C) Perform aperiodic motion D) None of the above Ans A 12) Transmissibility in a force excitation system is defined by the ratio of the A) Maximum excitation force to the force transmitted to the foundation B) Force transmitted to the foundation, to the maximum excitation force C) Maximum static deflection of the ass to the deflection of the foundation D) None of the above Ans B 13) Transmissibility in a support excitation system is defined by A) Ratio of absolute amplitude of the mass to the excitation amplitude of the support B) Reciprocal of (a) C) Ratio of the force transmitted to the foundation, to the equivalent force corresponding to maximum displacement excitation D) None of the above Ans B

14) The condition to be fulfilled in the design of spring for vibration isolation of a system where excitation is due to a rotating unbalance is A) ω ωn D) ω >> ωn Ans A 15) where springs of low damping are required for the purpose of vibration isolation, it will be most desirable to use A) Metallic springs B) Rubber pad C) Air springs D) Neoprene pads Ans A 16) Determine natural frequency of a system, which has equivalent spring stiffness of 30000 N/m and mass of 20 kg? A) 12.32 Hz B) 4.10 Hz C) 6.16 Hz D) None of the above Ans C 17) In damped free vibrations, which parameters indicate vibrations? A) Natural frequency B) Rate of decay of amplitude C) Both a. and b. D) None of the above Ans C 18) Which of the following relations is true for viscous damping? A) Force α relative displacement B) Force α relative velocity C) Force α (1 / relative velocity) D) None of the above Ans B 19) Eddy current damping is an example of _____ A) Coulomb damping B) Hysteresis damping C) Viscous damping D) Dry friction damping Ans C 20) According to which method, maximum kinetic energy at mean position is equal to maximum potential energy at extreme position? A) Energy method

B) Rayleigh's method C) Equilibrium method D) All of the above Ans B

1) In centrifugal pendulum absorber , the natural frequency in cycle per second can be given by A) Fn =N √(R/L) B) Fn =1/N √(R/L) C) Fn =N/2 √(R/L) D) Fn =N2 √(R/L) Ans A 2) According to the untuned dry fraction damper amplitude reduction will be A) Lesser if lesser amount of energy dissipated B) Greater if greater amount of energy dissipated C) Greater if lesser amount of energy dissipated D) Lesser if greater amount of energy dissipated Ans B 3) Dynamic vibration absorber is suitable for A) Constant speed machine B) Varying speed machine C) zero speed machine D) None of the above Ans A 4) The principal of mode vibration can be given by A) Two masses vibrate at Different frequency and in same phase B) Two masses vibrate at Different frequency and in Different phase C) Two masses vibrate at same frequency and in Different phase D) Two masses vibrate at same frequency and in same phase Ans D 5) Semi definite system having one of their natural frequency equal to A) Four B) Three C) Two D) Zero Ans D 6) The rotating shaft or rotor vibrates with excessive lateral vibration at angular speed at which occurs is called as A) rotating speed B) critical speed C) vibrating speed D) None of the above Ans B 7) Which of the following condition should be satisfied in the design of a vibration absorber ? A) Natural frequency of the auxiliary system should be equal to the natural frequency of the main system B) Natural frequency of the auxiliary system should be equal to the half natural frequency of the main system

C) Natural frequency of the auxiliary system should be fall in between natural frequency of the main system and the frequency of excitation D) Natural frequency of the auxiliary system should be twice natural frequency of the main system Ans A 8) Centrifugal absorber is used to reduce A) Centrifugal force in rotating system B) Torsional vibration of rotating system C) Vibration in linear system D) Transverse vibrations Ans B 9) Critical speed of shaft and disc system A) Is equal to natural frequency of the system in transverse vibration B) Is equal to natural frequency of the system in torsional vibration C) Is equal to natural frequency of the system in longitudinal vibration D) Bears no relationship to any of the system natural frequency Ans A 10) In most practical situation the speed of rotation of the shaft is usually A) Much below the critical speed B) Much above the critical speed C) Near about the critical speed D) Having no relationship with critical speed Ans B 11) Untuned viscous damper ( houdaille Damper) is used with variable speed machine being control by ratio can be given by A) (damper inertia) / (main system inertia) B) (main system inertia) / (damper inertia) C) (2 X damper inertia) / (main system inertia) D) (2 X main system inertia) / (damper inertia) Ans A 12) The two resonant frequency ratio (ω/ ω2) in a dynamic vibration absorber system for a mass ratio 0.2 are given by A) 0 ; 1.0 B) 0.801 ; 1.248 C) 0.458 ; 1.124 D) 0.642 ; 1.558 Ans B 13) In a 2-mass 3 spring vibrating system the two masses each are of 9.8 kg coupling spring is having a stiffness of 3430 N/m whereas the other two springs have each a stiffness of 8820 N/m. The two natural frequencies in rad /sec are A) 10 & 20 B) 20 & 30 C) 30 & 40

D) 40 & 50 Ans C 14) Frequency of centrifugal pendulum absorber is always proportional to A) Oscillating motion B) Transfer motion C) Speed of rotating body D) All of the above Ans C 15) Critical speed of shaft having a rotating disc in the middle is A) x/e = 1 / ( r^2 - 1 ) B) x/e = 1 / ( r^2 + 1 ) C) x/e = 1 / ( r^2 - 1^2 ) D) x/e = ( 1 + r) / ( r^2 – 1 ) Ans A 16) According to which method, maximum kinetic energy at mean position is equal to maximum potential energy at extreme position? A) Energy method B) Rayleigh's method C) Equilibrium method B) All of the above Ans B 17) The motion of a system executing harmonic motion with one natural frequency is known as _______ A) principal mode of vibration B) natural mode of vibration C) both a. and b. D)none of the above Ans C 18) What is meant by coupled differential equation? A) The differential equation in which only rectilinear motions exit B) The differential equation in which only angular motions exit C) The differential equation in which both rectilinear and angular motions exit D) None of the above Ans C 19) What is meant by node point? A) The point at which amplitude of vibration is maximum B) The point at which amplitude of vibration is minimum C) The point at which amplitude of vibration is zero D) None of the above Ans C

20) Which of the following statements is/are true? A) Torsional vibrations do not occur in a three rotor system, if rotors rotate in same direction B) Shaft vibrates with maximum frequency when rotors rotate in same direction C) Zero node behavior is observed in rotors rotating in opposite direction D) All of the above Ans A

Model Question Paper Subject Class Semester

: : :

Mechanical Vibration B. E. VIII

Q1. The motion completed during one time period is known as _______. A. period of vibration B. cycle C. frequency D. all of the above Ans: B Q2. When a rigid body is suspended vertically and it oscillates with a small amplitude under the action of the force of gravity, the body is known as A. simple pendulum B. torsional pendulum C. compound pendulum D. second’s pendulum Ans:C Q.3 The motion completed during one time period is known as _______. A. period of vibration B. cycle C. frequency D. all of the above Ans:B Q.4 Which of the following is a type of free vibration? A. Longitudinal vibrations B. Transverse vibrations C. Torsional vibrations D. A, B and C Ans:D Q.5 The maximum acceleration of a particle moving with simple harmonic motion is ____. A. ω B. ω.r C. ω / 2 π D. 2 π / ω Ans:B

Q.6 As per Energy Method, the summation of kinetic energy and potential energy must be ________ which is same at all the times. A. zero B. minimum C. maximum D. constant Ans:D Q.7 Equilibrium Method is in accordance with which of the following principle? A. Taylor's principle B. D'Alembert's principle C. Energy conservation principle D. None of the above Ans:B Q.8 Frequency is equal to ______. A. time period B. 1/time period C. *time period D. /time period Ans:B Q.9 When the particles of the shaft or disc move in a circle about the axis of the shaft, then the vibrations are known as ___________ . A. longitudinal vibrations B. transverse vibrations C. torsional vibrations D. none of these Ans:C Q.10 For the same dimensions of the shaft which of the following has the greater natural frequency? A. Transverse B. Longitudinal C. Depends on thickness D. Depends upon length Ans:B Q.11 A vertical spring-mass system has a mass of 0.5 kg and an initial deflection of 0.2 cm. Find the spring stiffness. A. 345 N/m B. 245 N/m C. 3452 N/m

D. 2452 N/m Ans:D Q.12 A system has a mass of 0.5 kg and spring stiffness of 2452 N/m. Find the natural frequency of the system. A. 5.14 Hz B. 9.14 Hz C. 11.14 Hz D. 28.14 Hz Ans:C Q.13 An increase in the mass moment of inertia results in ________ in vibration frequency. A. increase B. decrease C. unchanged D. none of the above Ans:B Q.14 The ratio of the force transmitted to the force applied is known as the ____________ of the spring support. A. isolation factor B. transmissibility ratio C. both A and B D. none of the above Ans:C Q.15 If the damper is not provided and the system is in resonance, which of the following is the correct isolation factor? A. 0 B. 0.5 C. 0.25 D. Infinite Ans:D Q.16 Calculate damped natural frequency, if a spring mass damper system is subjected to periodic disturbing force of 30 N. Damping coefficient is equal to 0.76 times of critical damping coefficient and undamped natural frequency is 5 rad/sec A. 3.99 rad/sec B. 2.13 rad/sec C. 4.12 rad/sec D. 3.24 rad/sec

Ans:D Q.17 At which frequency ratio, phase angle increases as damping factor increases? A. When frequency ratio is less than unity B. When frequency ratio is more than unity C. When frequency ratio is zero D. All of the above Ans:A Q.18 Consider the steady-state absolute amplitude equation shown below, if ω / ωn = √2 then amplitude ratio (X/Y) =? (X/Y) = √{1 + [ 2ξ (ω/ωn)]2} / √{[1 – (ω/ωn)2]2 + {2ξ (ω/ωn)2} A. 0 B. 1 C. less than 1 D. greater than 1 Ans:B Q.19 The equation m(d2 x/ dt2) + c (dx/dt) + Kx = F0 sin ωt is a second order differential equation. The solution of this linear equation is given as A. complementary function B. particular function C. sum of complementary and particular function D. difference of complementary and particular function Ans:C Q.20 The rate of decay of oscillations is known as....... A. critical damping B. damping coefficient C. transmissibility D. logarithmic decrement Ans:D Q.21 Two springs have spring stiffness of 1500 N/m and 2000 N/m respectively. If they are connected in series, what is the spring stiffness if they are replaced by an equivalent system.3500 N/m A. 3500 N/m B. 1166 N/m

C. 857.63 N/m D. None of the above Ans:C Q.22 Which among the following is the fundamental equation of S.H.M.? A. x + (k / m) x =0 B. x + ω 2x =0 C. x + (k/ m) 2 x =0 D. x 2 + ωx2 =0 Ans:B Q.23 Calculate coefficient of viscous damper, if the system is critically damped. Consider the following data: 1. Mass of spring mass damper system = 350 kg 2. Static deflection = 2 x 10–3 m 3. Natural frequency of the system = 60 rad/sec A. 100.5 x 10 3 N-s/m B. 80 x 103 N-s/m C. 42 x 103 N-s/m D. None of the above Ans:C Q.24 A vibrating machine of 100 kg is mounted on a rubber pad which has stiffness of 500 N/m. Determine force transmitted to the foundation if the unbalanced force 500 N acts on it. The frequency ratio (ω/ωn) is 1.5 and ξ = 0.5 A. 461.62 N B. 400.23 N C. 450 N D. Insufficient data Ans:A Q.25 According to D' Alembert's principle, m (d2 x/ dt2) + c (dx/dt) + Kx =0 is the differential equation for damped free vibrations having single degree of freedom. What will be the solution to this differential equation if the system is critically damped? A. x = (A + Bt) e– ωt B. x = X e – ξωt (sin ωdt + Φ) C. x = (A – Bt) e– ωt D. x = X e– ξωt (cos ω dt + Φ) Ans:A

Q.26 Which of the following vibro-meters have frequency ratio (ω/ωn) √2 is known as____

A. Amplification region B. Isolation region C. Spring controlled region D. None of the above Ans:B Q.28 Determine natural frequency of a system, which has equivalent spring stiffness of 30000 N/m and mass of 20 kg? A. 12.32 Hz B. 4.10 Hz C. 6.16 Hz D. None of the above Ans:C Q.29 According to which method, maximum kinetic energy at mean position is equal to maximum potential energy at extreme position? A. Energy method B. Rayleigh's method C. Equilibrium method D. All of the above Ans:B

Q.30 A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of √3k/m, the ratio of the amplitude of steady state response to the static deflection of the spring is __________

A. 0.2 B. 0.5 C. 0.8 D. None of the above Ans:B Q.31 Figure shows a single degree of freedom system. The system consists of a mass-less rigid bar OP hinged O and a mass m at end P. The natural frequency of vibration of the system is

A. B. C. D. Ans:A

Q.32 Which type of frequency measuring instrument has multiple reeds of different natural frequency to measure vibrations? A. Fullarton tachometer B. Frahm Tachometer C. Both A. and B. D. None of the above Ans:B Q.33 Eddy current damping is an example of _____

A. Coulomb damping B. Hysteresis damping C. Viscous damping D. Dry friction damping Ans:C Q.34 In the diagram sho...