Distance in one oscillation = 4ATherefore distance in 3/8 oscillation =3/2A= A+A/2Time to cover A distance is T/4 and time to cover A/2 distance is T/6So total time is 5T/12Where A =amplitude of oscillation

Introduction:
The period of an oscillator is the time taken for one complete oscillation. In this problem, we are given that the period of the oscillator is T. We need to determine the time it takes for the oscillator to complete 3/8th of its oscillation, starting from a fixed point.

Understanding the Problem:
The problem asks for the time taken to complete 3/8th of an oscillation. To solve this, we need to find the fraction of the period that corresponds to 3/8th of the oscillation.

Solution:
To find the time taken to complete 3/8th of an oscillation, we can use the fraction of the period that corresponds to this fraction of the oscillation.

Step 1: Finding the Fraction of the Period:
To find the fraction of the period corresponding to 3/8th of the oscillation, we can multiply the period T by the fraction 3/8.

Fraction of the period = (3/8) * T.

Step 2: Simplifying the Fraction:
To simplify the fraction, we can multiply the numerator and denominator by the same number to obtain an equivalent fraction with smaller values.

Multiplying the numerator and denominator by 3, we get:

Fraction of the period = (3/8) * T = (3 * T) / (8 * 1) = 3T / 8.

Step 3: Identifying the Answer:
From the simplified fraction, we can see that the time taken to complete 3/8th of an oscillation is 3T/8.

Therefore, the correct answer is option A) 3/8T.

Explanation:
Starting from a fixed point, the oscillator completes one full oscillation in time T. To find the time taken to complete a fraction of the oscillation, we can multiply the period T by the fraction.

In this case, the fraction we are interested in is 3/8th of the oscillation. By multiplying the period T by 3/8, we find that the time taken to complete 3/8th of an oscillation is 3T/8.

Hence, the correct answer is option A) 3/8T.