Question

(a) Define natural vibrations.
(b) How is this vibration different from damped vibrations in terms of their amplitudes?

Hint:

Natural = Ideal, Constant Amplitude. Damped = Real-world, Decreasing Amplitude. Forced = External driver, Constant Amplitude (at steady state).

Answer 1

(a) Definition of Natural Vibrations:
Natural vibrations (or free vibrations) are the periodic vibrations of a body that occur in the complete absence of any external resistive or driving forces. The body vibrates at its own characteristic frequency, known as its natural frequency.
(b) Difference from Damped Vibrations:
The key difference between natural vibrations and damped vibrations lies in the behavior of their amplitudes over time:
- Natural Vibrations: In an ideal scenario of natural vibrations, there is no energy loss. As a result, the amplitude of vibration remains constant indefinitely.
- Damped Vibrations: In damped vibrations, resistive forces (like friction or air resistance) are present. These forces dissipate the energy of the vibrating system. Consequently, the amplitude of vibration continuously decreases over time, eventually becoming zero.