From the study of subatomic particles to the laws of motion, Physics Topics offer insights into the workings of the world around us.
Is Free Vibration Natural Frequency?
A vibrating body always moves to and 1ro about an equilibrium position. At the instant when it is at the equilibrium position, there are no forces acting on the body. However, the body does not stop because of its inertia of motion. As
soon as it crosses the equilibrium position. a force acts on it. This force is always directed towards the equilibrium position and is called the restoring force.
If no force other than the restoring force acts on the body, or the effect of other forces is negligible, the body can vibrate without interruption, i.e., its vibration is a free or natural vibration. The amplitude of this vibration remains unchanged with passage of time.
Definition: If the effect of forces other than the restoring force is negligible on a vibrating body, its motion is called a free or natural vibration.
A body undergoing free vibration has a definite frequency, i.e., the body executes a fixed number of vibrations in unit time. It is called its natural frequency. The natural frequency (n0) depends on the density, shape and elasticity, etc. of the vibrating body. For example:
A simple pendulum: n0 = \(\frac{1}{T}\) = \(\frac{1}{2 \pi} \sqrt{\frac{g}{L}}\) ; so if g is constant, the natural frequency of a simple pendulum depends on its length L.
An elastic spring: n0 = \(\frac{1}{T}\) = \(\frac{1}{2 \pi} \sqrt{\frac{k}{m}}\) ; here the spring constant k is related to the elasticity of the material of the spring. It may be said that the natural frequency of the spring depends on the mass (m) hanging at the end of the spring and the elasticity of the material of the spring.
Every vibrating body such as a tuning fork, the string of a musical instrument, etc, has its characteristic natural frequency.