This set of Mechanical Vibrations Multiple Choice Questions & Answers (MCQs) focuses on “Rayleigh’s Energy Method”.

1. Rayleigh’s Energy method is based on which principle?

a) Principle of conservation of momentum

b) Principle of conservation of mass

c) Principle of conservation of energy

d) Principle of energy distortion

View Answer

Explanation: In a real dynamic system, the energy consisted is both Kinetic and Potential. So, the total energy must remain constant. T + U = Constant. This signifies the principle of conservation of energy.

2. What is the value of potential energy for a simple spring-mass system?

a) Zero

b) Varies from point to point

c) Equal to kinetic energy

d) Equal to the total energy

View Answer

Explanation: In a spring-mass system potential energy is zero when it passes through the static equilibrium point. It then goes to the maximum at the extreme ends.

3. In a spring-mass system, what is the value of kinetic energy at the extreme points?

a) Infinite

b) Zero

c) Varies exponentially

d) Varies linearly

View Answer

Explanation: At the mean position the kinetic energy is maximum and at extreme positions, it experiences a change in direction which is opposite to the initial direction of motion. So kinetic energy falls to zero at the extreme position.

4. Rayleigh’s energy method can be used for __________

a) Multi-mass system

b) System with cam-follower mechanism

c) System having redundant links

d) Discrete systems

View Answer

Explanation: The Rayleigh’s energy method can be used to find out the angular velocity for multi-mass of for distributed mass systems.

5. What is the necessary condition for applying Rayleigh’s Energy method?

a) The momentum of each point has to be known

b) The motion of each point in the system has to be known

c) The angular acceleration should be constant for all points

d) The angular momentum should be the same for all points

View Answer

Explanation: The motion of each point in the system needs to be known for calculation of the angular velocity using Rayleigh’s Energy method.

6. What is the necessary degree of freedom of a system to apply Rayleigh’s Method for calculation?

a) 1

b) 2

c) 3

d) 4

View Answer

Explanation: Only one coordinate is necessary for defining the motion of various masses with simple rigid links, levers or gears. The motion of various masses can be expressed in terms of the motion ẋ of some specific point.

7. What is the value of angular velocity (ω_{n}) of a spring-mass system? (k = spring stiffness, m_{eff} =effective mass, m = initial mass)

a) \(\sqrt{\frac{k}{m}} \)

b) \(\sqrt{\frac{k}{m_{eff}}} \)

c) \(\sqrt{\frac{m}{k}} \)

d) \(\sqrt{\frac{m_{eff}}{k}} \)

View Answer

Explanation: The value of the angular velocity of a spring mass system is \(\sqrt{\frac{k}{m_{eff}}} \). Effective mass stands for the net mass acting from the point where a link is fixed and not from the center of mass.

8. The kinetic energy of a simple spring mass system can be written as __________

a) ½ m_{eff} ẋ^{2}

b) ¼ m_{eff} ẋ^{2}

c) ½ m_{eff} \(\ddot{x}\)

d) K \(\ddot{x}\)^{2}

View Answer

Explanation: The total kinetic energy stored in a simple spring mass system can be equated as

T = ½ m

_{eff}ẋ

^{2}. Here m

_{eff}stands for the effective mass of the system and ẋ stands for the first degree differentiation of the displacement x.

9. When the mass of the spring (m_{spring}) is considered, what is the equation for the angular velocity (ω_{n}) of natural vibration?

a) \(\sqrt{\frac{k}{m+\frac{m_{spring}}{3}}} \)

b) \(\sqrt{\frac{k}{m+\frac{m_{spring}}{4}}} \)

c) \(\sqrt{\frac{3 k}{m+ m_{spring}}} \)

d) \(\sqrt{\frac{4 k}{m+ m_{spring}}}\)

View Answer

Explanation: usually the mass of the spring is not considered while calculation of angular velocity. But when the mass of spring is considered then the equation of angular velocity (ω

_{n}) = \(\sqrt{\frac{k}{m+\frac{m_{spring}}{3}}} \)

10. Rayleigh’s Method is used with a reasonable assumption for the shape of vibration amplitude.

a) True

b) False

View Answer

Explanation: Rayleigh’s Method is based on the energy consisted is both Kinetic and Potential. So, the total energy must remain constant. T + U = Constant, in real dynamics. But it uses reasonable assumptions for the shape of vibration amplitude.

**Sanfoundry Global Education & Learning Series – Mechanical Vibrations.**

To practice all areas of Mechanical Vibrations, __ here is complete set of Multiple Choice Questions and Answers__.