Definitions

1. Periodic motion –A motion which repeats itself after equal intervals of time is known as periodic motion. Any periodic can be represented by function x(t) in the period T, the function x(t) is called periodic function

2. Time Period – Time taken to complete one cycle is called periodic function.

3. Frequency –The number of cycles per unit time is known as frequency

4. Natural frequency – When no external force acts on the system after giving it an initial displacement , the body vibrates. These vibration are called free vibrations and their frequency as natural frequency. It is expressed in c/s or hertz

5. Amplitude – The max displacement of a vibrating body from its equilibrium position is called amplitude

6. Fundamental mode of vibration – The fundamental mode of vibration of a system is the mode having the lowest natural frequency

7. Resonance – When the frequency of external exitation is equal to the natural frequency of a vibrating body, the amplitude of vibration becomes excessively large. This concept is known as resonace

8. Mechanical System – The system consisting of mass shiftness and damping are known as mechanical system.

9. Continuous and Discrete system – Most of mechanical system include elastic members which have infinite number of degree of freedom. Such system are called continuous system or distributed system. Eg. Cantilever,Simply Supported beam System with finite number of degrees of freedom are called discrete system

10. Degree of freedom – The minimum no. of independent co-ordinates required to specify the motion of a system at any instant is known as degree of freedom of the system

11. Simple harmonic motion – A periodic motion of a particle whose acceleration is always directed towards the mean position and is proportional to its distance from the mean position is known as SHM. It may also defined as the motion of a projection of a particle moving round a circle with uniform angular velocity on a diameter.

12. Phase difference – the angle between two rotating vectors representing simple harmonic motion of the same frequency