Hi,
Mechanical Vibration is a good subject to study for getting job in research field as well as for scoring in GATE and of course in semester examination as well, but you need to have good books for this, so here I am going to share with you best books for mechanical vibration for GATE and also for semester exams.
✅MECHANICAL VIBRATIONS by VP Singh
✅Mechanical Vibrations 4e by Pearson Education India
✅👉👍GATE Mechanical Previous Year Questions with Answers Book [Latest Edition]
Overview and Understanding Mechanical Vibration Subject for GATE –
In general, there are 1 or 2 questions we have seen so far in GATE, few of them I will share with you below, for your ease of understanding difficultly level of questions, which will be awesome right.
🔥Best Books for GATE Mechanical Engineering with 28 Tips to Get Good Score in the Exam.
Syllabus for GATE- Vibrations: Free and forced vibration of single degree of freedom systems, effect of damping; vibration isolation; resonance; critical speeds of shafts.
All Important Formulas of Mechanical Vibration for GATE-
👉👉 Don’t just watch the video, take action to see result.
Mechanical Vibration GATE Previous Questions with Detail Solutions/Answers-
5 Tips for Preparing Mechanical Vibration for GATE-
Tip 1- Understand basics, prepare your short notes, don’t download and get print out of it, which is not recommended.
Tip 2- Clear Basic Concepts and solve few simple only formula based numerical, preferably solve ESE numerical problems.
Tip 3- Next step is to solve GATE Previous year questions, here is the catch, if any problem you unable to solve don’t see solution just explore more things in the text book to solve it, when to see solution? Until you have tried your maximum to solve that or those problems.
Tip 4- Figure out your weak points and put more focus on those points, so that with time you will become stronger.
Tip 5- Biggest Mistakes by 90% Aspirants, they don’t write test series right way, means even those write they don’t just focus on test series to get good score or where they are making mistakes, you need to focus on all these to get success in GATE like exam.
3 Tips to Avoid Getting Backlog in Semester Examination-
Tip 1- Study from beginning of the semester, one of the biggest mistakes student made they don’t study from beginning, so I always recommend you to start in the beginning.
Tip 2- Prepare your own notes and always plan according to your examination pattern so that you can do better at the end while doing revision.
Tip 3- Solve numerical from books as well as from previous year papers, this is the reason students unable to solve questions of GATE as well as in the semester examinations, yeah for semester examination you need to prepare derivation also.
Avoid These Mistakes for GATE Preparation-
Most Important Topics of Mechanical Vibration for GATE-
Yes, there are certainly few topics are most important for GATE examination point of view-
- Natural frequency of systems
- Damping Factor, Critical Damping
- Transmissibility Ratio
- Whirling of Shaft
- Magnification factor
- Critical speed
- 🔥Special Cases
Questions Asked in GATE Previous Years from Mechanical Vibration-
Q. (1) In a single degree of freedom under damped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains under damped. Which one of the following statements is ALWAYS true?
(A) Transmissibility will increase.
(B) Transmissibility will decrease.
(C) Time period of free oscillations will increase.
(D) Time period of free oscillations will decrease.
Q. (2) The damping ratio for a viscously damped spring mass system, governed by the relationship
Q. (3) A machine of mass m = 200 kg is supported on two mounts, each of stiffness k = 10 kN/m. The machine is subjected to an external force (in N) F(t) = 50 cos 5t. Assuming only vertical translatory motion, the magnitude of the dynamic force (in N) transmitted from each mount to the ground is ______ (correct to two decimal places).
Q. (4) A mass-spring-dashpot system with mass m = 10 kg, spring constant k = 6250 N/m is excited by a harmonic excitation of 10 cos(25t) N. At the steady state, the vibration amplitude of the mass is 40 mm. The damping coefficient ( c, in N.s/m) of the dashpot is ______
Q. (5) The radius of gyration of a compound pendulum about the point of suspension is 100 mm. The distance between the point of suspension and the centre of mass is 250 mm. Considering the acceleration due to gravity is 9.81 m/s^2 , the natural frequency (in radian/s) of the compound pendulum is ___________
Q. (6) The equation of motion for a spring-mass system excited by a harmonic force is
where M is the mass, K is the spring stiffness, F is the force amplitude and ω is the angular frequency of excitation. Resonance occurs when ω is equal to
Q. (7) As shown in Figure, a mass of 100 kg is held between two springs. The natural frequency of vibration of the system, in cycles/s is
(A) 1 2π
(B) 5 π
(C) 10 π
(D) 20
Q. (8) A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor (ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mm.
Q. (9) The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1 mm. Assume the acceleration due to gravity g =10 m/s2. The natural frequency of this spring-mass system (in rad/s) is_____________
Q. (10) A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of (3k/m)^(1/2), the ratio of the amplitude of steady state response to the static deflection of the spring is……..
Q. (11) A single degree of freedom system has a mass of 2 kg, stiffness 8 N/m and viscous damping ratio 0.02. The dynamic magnification factor at an excitation frequency of 1.5 rad/s is _______
Q. (12) The damping ratio of a single degree of freedom spring-mass-damper system with mass of 1 kg, stiffness 100 N/m and viscous damping coefficient of 25 N.s/m is _______
Q. (13) Which of the following statements are TRUE for damped vibrations?
P. For a system having critical damping, the value of damping ratio is unity and system does not undergo a vibratory motion.
Q. Logarithmic decrement method is used to determine the amount of damping in a physical system.
R. In case of damping due to dry friction between moving surfaces resisting force of constant magnitude acts opposite to the relative motion.
S. For the case of viscous damping, drag force is directly proportional to the square of relative velocity.
(A) P and Q only
(B) P and S only
(C) P, Q and R only
(D) Q and S only
Q. (14) A precision instrument package (m = 1 kg) needs to be mounted on a surface vibrating at 60 Hz. It is desired that only 5% of the base surface vibration amplitude be transmitted to the instrument. Assume that the isolation is designed with its natural frequency significantly lesser than 60 Hz, so that the effect of damping may be ignored. The stiffness (in N/m) of the required mounting pad is _____
Q. (16) A single-degree-freedom spring-mass system is subjected to a sinusoidal force of 10 N amplitude and frequency ω along the axis of the spring. The stiffness of the spring is 150 N/m, damping factor is 0.2 and the undamped natural frequency is 10ω. At steady state, the amplitude of vibration (in m) is approximately
(A) 0.05
(B) 0.07
(C) 0.70
(D) 0.90
Q. (17) A single degree of freedom mass-spring-viscous damper system with mass m, spring constant k and viscous damping coefficient q is critically damped. The correct relation among m, k, and q is ……….
Q. (18) In a spring-mass system, the mass is m and the spring constant is k. The critical damping coefficient of the system is 0.1 kg/s. In another spring-mass system, the mass is 2 m and the spring constant is 8 k. The critical damping coefficient (in kg/s) of this system is ____________
Q. (19) A mass m is attached to two identical springs having spring constant k as shown in the figure. The natural frequency ω of this single degree of freedom system is
Q. (20)If two nodes are observed at a frequency of 1800 rpm during whirling of a simply supported long slender rotating shaft, the first critical speed of the shaft in rpm is
(A) 200
(B) 450
(C) 600
(D) 900
Q. (21) A uniform rigid rod of mass m = 1 kg and length L = 1 m is hinged at its center and laterally supported at one end by a spring of spring constant k = 300 N/m. The natural frequency ωn in rad/s is
(A) 10
(B) 20
(C) 30
(D) 40
Q. (22) A point mass is executing simple harmonic motion with an amplitude of 10 mm and frequency of 4 Hz. The maximum acceleration (m/s 2 ) of the mass is _______
Q. (23) A disc of mass m is attached to a spring of stiffness k as shown in the figure. The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is
Q. (24) What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by k1 and k2 as shown below.
Q. (25) In vibration isolation, which one of the following statements is NOT correct regarding Transmissibility (T)?
(A) T is nearly unity at small excitation frequencies
(B) T can be always reduced by using higher damping at any excitation frequency
(C) T is unity at the frequency ratio of 2
(D) T is infinity at resonance for undamped systems
Q. (26) An automotive engine weighing 240 kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 16MN/m while the stiffness of each rear spring is 32MN/m. The engine speed (in rpm), at which resonance is likely to occur, is
(A) 6040 (B) 3020 (C) 1424 (D) 955
Q. (27) The natural frequency of a spring-mass system on earth is ωn. The natural frequency of this system on the moon (gm =ge/6) is
(A) ωn (B)0.408ωn (C) 0.204ωn (D) 0.167ωn
Q. (28) Critical damping is the
(A) Largest amount of damping for which no oscillation occurs in free vibration
(B) Smallest amount of damping for which no oscillation occurs in free vibration
(C) Largest amount of damping for which the motion is simple harmonic in free vibration
(D) Smallest amount of damping for which the motion is simple harmonic in free vibration
Q. (29) Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the exciting force is
(A) 0
(B) 45
(C) 90
(D) 135
Q. (30) A concentrated mass m is attached at the center of a rod length 2L as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of vibration, neglecting the weights of the rod and spring, the un-damped natural frequency of the system is
Q. (31) The natural frequency of the system shown below is
Q. (32) A flexible rotor shaft system comprises of a 10 kg rotor disc placed in the middle of a massless shaft of diameter 30 mm and length 500 mm between bearing (shaft is being taken massless as the equivalent mass of the shaft is included in the rotor mass) mounted at the ends. The bearings are assumed to simulate simply supported boundary conditions. The shaft is made of steel for which the value of E is 2.1 × 1011 Pa. What is the critical speed of rotation of the shaft?
(A) 60 Hz (B) 90 Hz (C) 135 Hz (D) 180 Hz
Q. (33) A vibratory system consists of a mass 12.5 kg, a spring of stiffness 1000 N/m, and a dashpot with damping coefficient of 15 Ns/m. The value of critical damping of the system is:
(A) 0.223 Ns/m
(B) 17.88 Ns/m
(C) 71.4 Ns/m
(D) 223.6 Ns/m
Q. (34) The value of logarithmic decrements is:
(A) 1.35
(B) 1.32
(C) 0.68
(D) 0.66
Q. (35)
Q. (36) For an under damped harmonic oscillator, resonance
(A) occurs when excitation frequency is greater than undamped natural frequency
(B) occurs when excitation frequency is less than undamped natural frequency
(C) occurs when excitation frequency is equal to undamped natural frequency
(D) never occurs
Q. (37) In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1 kN/m. By introducing a damper, the frequency of oscillation is found to be 90% of the original value. What is the damping coefficient of the damper?
(A) 1.2 Ns/m (B) 3.4 Ns/m (C) 8.7 Ns/m (D) 12.0 Ns/m
Q. (38) A mass M, of 20 kg is attached to the free end of a steel cantilever beam of length 1000 mm having a cross-section of 25 × 25 mm. Assume the mass of the cantilever to be negligible and E steel = 200 GPa. If the lateral vibration of this system is critically damped using a viscous damper, the damping constant of the damper is
(A) 1250 Ns/m (B) 625 Ns/m (C) 312.50 Ns/m (D) 156.25 Ns/m
Q. (39) A vibrating machine is isolated from the floor using springs. If the ratio of excitation frequency of vibration of machine to the natural frequency of the isolation system is equal to 0.5, the transmissibility of ratio of isolation is
(A) 1/2
(B) 3/4
(C) 4/3
(D) 2
Q. (40) Consider the system of two wagons shown in Figure. The natural frequencies of this system are
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