# Free Vibration of a Spring Mass System

1.1 Objective of the virtual experiment

To obtain the natural frequency of the spring-mass system and to observe its response to an initial disturbance and the type of the system based on damping ratio.

1.2  Source for this virtual experiment

Experimentally obtained data is used in this virtual experiment to obtain the results.

1.3  Basic Terminology

1.3.1 Free vibration:  Free vibration takes place when a system oscillates under the action of forces inherent in the system itself due to initial disturbance, and when the externally applied forces are absent. The system will oscillates about one of its static-equilibrium positions. Basically there are two types of systems. They are the discrete and continuous systems. In the case of discrete systems, the physical properties are discrete quantities and the system behavior is described by ordinary differential equations. The system has finite number of degrees-of-freedom whereas in the case of continuous system the physical properties are function of spatial co-ordinates and the system behavior is described by partial differential equations and has infinite number of degrees-of-freedom. In other words, a system can be considered as discrete in which the whole mass of the system is lumped at some points and in case of continuous system the mass is distributed over the entire length of the system. An n -degrees-of-freedom system is governed by n coupled differential equations and has n natural frequencies. So the discrete system has finite number of natural frequencies and the continuous system has infinite number of natural frequencies. The system under free vibration will vibrate at one or more of its natural frequencies, which are properties of the dynamical system, established by its mass and stiffness distribution.

1.3.2 Frequency: The number of oscillations completed per unit time is known as frequency of the system.

1.3.3 Natural Frequency: The frequency of free vibration of a system is called Natural Frequency of that particular system.

1.3.4 Damping: The resistance to the motion of a vibrating body is called Damping. In actual practice there is always some damping (e.g., the internal molecular friction, viscous damping, aero dynamical damping, etc.) present in the system which causes the gradual dissipation of vibration energy and results in gradual decay of amplitude of the free vibration. Damping has very little effect on natural frequency of the system, and hence, the calculations for natural frequencies are generally made on the basis of no damping. Damping is of great importance in limiting the amplitude of oscillation at resonance.