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

Step 1: Understanding the Concept:
A body capable of vibrating will do so with a specific frequency if it is displaced from its mean position and released.
Step 2: Detailed Explanation:
Natural (or free) vibrations are the periodic oscillations of a body when it is displaced from its equilibrium position and allowed to vibrate freely in the absence of any external force, such as air resistance or friction.
In such a state, the body vibrates with its natural frequency, which depends on its shape, size, and material.
Step 3: Final Answer:
Natural vibrations are vibrations of constant amplitude and frequency in a vacuum or a medium with no resistance.
(b)
Step 1: Detailed Explanation:
1. Natural Vibrations: In an ideal vacuum where there is no resistance, the energy of the vibrating body remains constant. Therefore, the amplitude of vibration remains constant over time.
2. Damped Vibrations: In the presence of a medium (like air), resistive forces do work against the moving body, converting its mechanical energy into heat. As energy is lost, the amplitude of the vibrations continuously decreases until the body stops.
Step 2: Final Answer:
Natural vibrations have a constant amplitude, whereas damped vibrations have an amplitude that decreases with time.