The formula to calculate the periodic time for simple harmonic motion (SHM) is:
\[ T_p = 2 \pi \sqrt{\frac{d}{g}} \]
Where:
Time period SHM is the time required for the periodic motion.
Total displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
Acceleration due to gravity is the acceleration gained by an object because of gravitational force.
Let's assume the following values:
Using the formula:
\[ T_p = 2 \pi \sqrt{\frac{0.0154}{9.8}} \approx 0.249073309245041 \, \text{seconds} \]
The periodic time for SHM is approximately 0.249073309245041 seconds.
| Total Displacement (m) | Acceleration due to Gravity (m/s²) | Periodic Time (s) |
|---|---|---|
| 0.01 | 9.5 | 0.203853449952 |
| 0.01 | 9.6 | 0.202788933799 |
| 0.01 | 9.7 | 0.201740921957 |
| 0.01 | 9.8 | 0.200708992315 |
| 0.01 | 9.9 | 0.199692737723 |
| 0.01 | 10 | 0.198691765316 |
| 0.012 | 9.5 | 0.223310265928 |
| 0.012 | 9.6 | 0.222144146908 |
| 0.012 | 9.7 | 0.220996107456 |
| 0.012 | 9.8 | 0.219865685171 |
| 0.012 | 9.9 | 0.218752434042 |
| 0.012 | 10 | 0.217655923708 |
| 0.014 | 9.5 | 0.241202654795 |
| 0.014 | 9.6 | 0.239943102297 |
| 0.014 | 9.7 | 0.238703077963 |
| 0.014 | 9.8 | 0.237482082345 |
| 0.014 | 9.9 | 0.236279633695 |
| 0.014 | 10 | 0.235095267171 |
| 0.016 | 9.5 | 0.257856484292 |
| 0.016 | 9.6 | 0.256509966032 |
| 0.016 | 9.7 | 0.255184324259 |
| 0.016 | 9.8 | 0.253879025038 |
| 0.016 | 9.9 | 0.252593553360 |
| 0.016 | 10 | 0.251327412287 |
| 0.018 | 9.5 | 0.273498102924 |
| 0.018 | 9.6 | 0.272069904635 |
| 0.018 | 9.7 | 0.270663849204 |
| 0.018 | 9.8 | 0.269279370308 |
| 0.018 | 9.9 | 0.267915921697 |
| 0.018 | 10 | 0.266572976290 |