When an oscillator completes 100 oscillations its amplitude reduced to ⅓ of initial values. What will be amplitude, when it completes 200 oscillations :

• A) ⅛
• B) ⅔
• C) ⅙
• D) ⅑

To determine the amplitude of the oscillator after it completes 200 oscillations, we first need to understand how the amplitude decreases with each set of oscillations. Given that the amplitude reduces to ⅓ of its initial value after 100 oscillations, we can analyze the pattern of reduction.

Amplitude Reduction Pattern

After 100 oscillations:

• Amplitude = Initial Amplitude × (1/3)

Now, we need to find the amplitude after 200 oscillations. The reduction appears to follow a consistent pattern. After another 100 oscillations (for a total of 200), we can apply the same reduction factor:

Calculating the Amplitude After 200 Oscillations

After the second set of 100 oscillations:

• Amplitude = (Amplitude after 100 oscillations) × (1/3)
• Amplitude = (Initial Amplitude × (1/3)) × (1/3) = Initial Amplitude × (1/3)²

Calculating (1/3)² gives us:

• (1/3)² = 1/9

Final Amplitude

Thus, after 200 oscillations, the amplitude will be:

• Amplitude = Initial Amplitude × (1/9)

From the options provided, the correct answer is:

• D) ⅑