For a simple pendulum, the time taken to complete one full oscillation (one complete to and fro swing) is known as what quantity?

Introduction / Context:
This question is about simple harmonic motion and pendulums. A simple pendulum swings back and forth about its mean position. One complete oscillation is a full to and fro motion. In describing such periodic motions, physicists use a particular term for the time taken to complete one cycle. Recognising this term is essential for solving problems involving frequency and timing of oscillations.

Given Data / Assumptions:

• The system is a simple pendulum swinging in a vertical plane.
• One oscillation means going from one extreme position to the other extreme and back again.
• We are asked for the name of the time taken for one complete oscillation.
• Options include maximum speed, average speed, time period and time interval.

Concept / Approach:
In periodic motion, the time taken to complete one full cycle is called the time period, usually denoted by T. For a pendulum, this is the time between successive passages through the same extreme position in the same direction or between successive crossings of the mean position in the same direction. Maximum speed and average speed are different concepts related to velocity, while time interval is a general term for any difference in time, not specifically one cycle. Therefore, time period is the correct answer.

Step-by-Step Solution:
Step 1: Visualise the pendulum bob moving from the left extreme to the right extreme and back to the left extreme. Step 2: Define one complete oscillation as such a full to and fro motion about the mean position. Step 3: The time taken for this one oscillation is a standard quantity in periodic motion, called the time period T. Step 4: Maximum speed refers to the highest speed reached during motion, which usually occurs at the mean position, not to the duration of a cycle. Step 5: Average speed is the total distance travelled divided by total time taken and is again not specific to one cycle definition. Step 6: Time interval is a generic term for any duration between two events and does not specifically refer to one full oscillation. Step 7: Conclude that the correct term for the time for one complete oscillation is time period.

Verification / Alternative check:
In formulas for a simple pendulum, such as T = 2 * π * √(L / g), T denotes the time period. Experimental measurements of pendulums involve measuring the time for multiple oscillations and then dividing by the number of oscillations to estimate T. For example, timing 20 swings and dividing the total time by 20 yields the time period. These standard practices and formulas consistently use time period for a single oscillation, confirming the answer.

Why Other Options Are Wrong:
Maximum speed describes how fast the bob moves at its fastest point and is measured in m/s, not in seconds as time is. Average speed over one or more oscillations is a different quantity and again is not the name for the duration of a single cycle. Time interval is too general and can refer to any duration; it is not the standard technical term in the context of periodic motion.

Common Pitfalls:
Some students use time interval and time period interchangeably in casual language. In physics, time period has a very specific meaning tied to periodic or oscillatory motion. Always associate the word period with cycles and oscillations. This habit will help you avoid confusion in questions dealing with pendulums, springs, electrical oscillations and waves.

Final Answer:
The time for one complete oscillation of a pendulum is called its Time period.