Question

an oscillator executes oscillations in a medium. it is found that the amplitude becomes one-third that of the initial amplitude after 100 oscillations. what will be the amplitude after 100 more oscillations take the initial amplitude as a0.

Answer 1

The amplitude after 100 more oscillations would be one-sixth of the initial amplitude, or a₀/6.

Step-by-step explanation:

An oscillator executes oscillations in a medium. In this case, the amplitude becomes one-third of the initial amplitude after 100 oscillations.

To find the amplitude after 100 more oscillations, we can consider the concept of energy in a simple harmonic oscillator. The energy is proportional to the square of the amplitude.

Since the amplitude becomes one-third of the initial amplitude after 100 oscillations, we can write the equation:

(1/3)^2 = (a/a₀)^2 = (100/200)^2

Solving for 'a', the amplitude after 100 more oscillations, we have:

a = (1/3) * (a₀/2)

= a₀/6

Therefore, the amplitude after 100 more oscillations would be one-sixth of the initial amplitude, or a₀/6.