To determine the periodic time of the simple pendulum, we can analyze the situation described. A seconds pendulum has a period of 2 seconds, meaning it completes one full oscillation in that time. Since the simple pendulum starts vibrating in phase with the seconds pendulum, we can infer that it will also have a periodic time close to 2 seconds.
Understanding the Phase Relationship
After 18 seconds, both pendulums are again in phase. This indicates that the simple pendulum has completed a certain number of oscillations that align with the seconds pendulum's oscillations.
Calculating the Periodic Time
- The seconds pendulum completes 9 full oscillations in 18 seconds (since 18 seconds ÷ 2 seconds/oscillation = 9 oscillations).
- Let the periodic time of the simple pendulum be T seconds.
- For the simple pendulum to also be in phase after 18 seconds, it must complete a whole number of oscillations.
Let’s denote the number of oscillations of the simple pendulum as N. The relationship can be expressed as:
18 seconds = N × T
Since the simplest case is when N = 9 (the same as the seconds pendulum), we can set:
18 seconds = 9 × T
Solving for T gives:
T = 18 seconds ÷ 9 = 2 seconds
Final Result
The periodic time of the simple pendulum is therefore 2 seconds.
