What is the period of a simple pendulum with a length of 2.25 m on each of the four given planets? Use the acceleration due to gravity on the "surface" of each planet given in the table. Mercury Venus Mars Jupiter Saturn Uranus Neptune 3.70 m/s? | 8.87 m/s² | 3.71 m/s? | 23.1 m/s? | 10.4 m/s? | 8.87 m/s²| 11.0 m/s? Jupiter: Saturn: S Uranus: Neptune: S S
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
![### Question 23 of 25
**Question:**
What is the period of a simple pendulum with a length of 2.25 m on each of the four given planets? Use the acceleration due to gravity on the "surface" of each planet given in the table.
**Table:**
| Planet | Gravity (m/s²) |
|----------|-----------------|
| Mercury | 3.70 m/s² |
| Venus | 8.87 m/s² |
| Mars | 3.71 m/s² |
| Jupiter | 23.1 m/s² |
| Saturn | 10.4 m/s² |
| Uranus | 8.87 m/s² |
| Neptune | 11.0 m/s² |
**Solution Fields:**
- Jupiter: ______ s
- Saturn: ______ s
- Uranus: ______ s
- Neptune: ______ s
**Explanation:**
To calculate the period (T) of a simple pendulum, we use the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
Where:
- \( T \) is the period,
- \( L \) is the length of the pendulum (given as 2.25 meters),
- \( g \) is the acceleration due to gravity on the surface of the respective planet.
### Sample Calculation:
For Jupiter, where \( g = 23.1 \, \text{m/s}^2 \):
\[ T = 2\pi \sqrt{\frac{2.25}{23.1}} \]
Please fill in the calculated period for each planet in the provided solution fields. Use the formula and the gravitational acceleration values from the table to compute your answers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5039f9f1-9031-4cf0-b840-7355f91f2cd2%2F6915008a-db7d-4288-942d-a69d606a4528%2F9hlkpuh.png&w=3840&q=75)
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