The formula to calculate the Minimum Periodic Time of SHM for a Compound Pendulum is:
\[ t_p = 2\pi \sqrt{\frac{2k_G}{g}} \]
The Minimum Periodic Time of SHM is the time required for one complete cycle of simple harmonic motion for a compound pendulum. It is calculated based on the radius of gyration and the acceleration due to gravity.
Let's assume the following values:
Using the formula:
\[ t_p = 2\pi \sqrt{\frac{2 \cdot 0.048}{9.8}} \approx 0.621874067737446 \, \text{seconds} \]
The Minimum Periodic Time of SHM is approximately 0.621874067737446 seconds.
| Radius of Gyration (meters) | Minimum Periodic Time (seconds) |
|---|---|
| 0.04 | 0.567690758045491 |
| 0.042 | 0.581709924798243 |
| 0.044 | 0.595399090062532 |
| 0.046 | 0.608780515691661 |
| 0.048 | 0.621874067737446 |
| 0.05 | 0.634697562594052 |
| 0.052 | 0.647267051379370 |
| 0.054 | 0.659597055511816 |
| 0.056 | 0.671700763345086 |
| 0.058 | 0.683590195451108 |