# Free Vibration of a Viscously Damped Single DOF System

1.1 Objective of the virtual experiment

To analyze the free vibration response of a system at various damping conditions.

1.2 Basic Terminology

1.2.1 Periodic Motion: A motion which repeats itself after equal intervals of time.

1.2.2 Free vibration: It 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 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.

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

1.2.4 Amplitude: The maximum displacement of a vibrating body from its equilibrium position.

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

1.2.6 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.

1.2.7 Fundamental Mode of Vibration: The fundamental mode of vibration of a system is the mode having the lowest natural frequency.

1.2.8 Degrees Of Freedom: The minimum number of independent coordinates needed to describe the motion of a system completely, is called the degrees-of-freedom of the system. If only one coordinate is required, then the system is called as single degree-of-freedom system.

1.2.9 Simple Harmonic Motion: The motion of a body to and fro about a fixed point is called simple harmonic motion. The motion is periodic, and its acceleration is always directed towards the mean position and is proportional to its distance from mean position. The motion of a simple pendulum is an example of simple harmonic motion.