Seconds pendulum — beats (oscillations) per second: A seconds pendulum has a time period of 2 s. How many oscillations (beats) per second does it execute?

Introduction / Context:
A seconds pendulum is defined so that one complete oscillation takes 2 seconds. Converting period to frequency (oscillations per second) is a straightforward application of simple harmonic motion relations.

Given Data / Assumptions:

• Time period T = 2 s.
• Small-angle approximation so the motion is nearly simple harmonic.
• One “beat” here means one full oscillation (to and fro).

Concept / Approach:

The relationship between period and frequency is f = 1 / T. Therefore, for T = 2 s, the frequency is 0.5 Hz, which is 0.5 oscillations (beats) per second.

Step-by-Step Solution:

Verification / Alternative check:

In 10 seconds, number of oscillations = time / period = 10 / 2 = 5. That is consistent with 0.5 per second.

Why Other Options Are Wrong:

(b)–(e) correspond to shorter periods not matching a seconds pendulum.

Common Pitfalls:

Counting half-oscillations as beats; mixing up time period and frequency units.

Final Answer:

0.5 beat per second