The period of the pendulum T (in s) is given below, where L-length of pendulum (in m), g-9.8 m/s². - 2 √ T= 2TA 1. Draw a free body diagrams of a pendulum while in motion. Rf = restoring force T= tension w = weight T 0. 2000 吧 W Data and Calculations Table 1 Mass (kg) 0.0500 0.1000 T₁(s) 1.9175 S 1.9293 1.9261s T₂(s) 1.91445 1.9911 s 1.9376 s 7 Error Length L= 87 cm = 0.87 m T3(s) Taverage(s) 1.9139 1.9153 s 1.92785 1.94945 1.9305 1.9314. 1.9153-2 x 100 2 = -4.24 S -4.24 -2.53 -3.43 @1.9494-2x100 2 = -2.53 S 2. Calculate the period T for the length that was used Tstandard- punto à from the stope %error=ITaverage -Tstandard I/Tstandard x 100=_ % Error 5. Does the period depend on the mass of the pendulum? Explain.
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.
![**Understanding Pendulum Motion: Calculations and Analysis**
The period of a pendulum \( T \) (in seconds) is determined by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where:
- \( L \) = Length of the pendulum (in meters)
- \( g \) = Acceleration due to gravity (9.8 m/s\(^2\))
1. **Conceptual Diagram**
- A free body diagram of a pendulum in motion is illustrated.
- Forces acting on the pendulum:
- \( T \) = Tension in the string
- \( W \) = Weight of the pendulum
- \( RF \) = Restoring force
2. **Data and Calculations - Table 1**
| Mass (kg) | \( T_1 \)(s) | \( T_2 \)(s) | \( T_3 \)(s) | \( T_{\text{average}} \) (s) | % Error |
|-----------|-------------|-------------|-------------|------------------------------|---------|
| 0.0500 | 1.9175 | 1.9144 | 1.9139 | 1.9153 | -4.24 |
| 0.1000 | 1.9293 | 1.9911 | 1.9278 | 1.9494 | -2.53 |
| 0.2000 | 1.9261 | 1.9376 | 1.9305 | 1.9314 | -3.43 |
3. **Experimental Setup**
- Length \( L \) = 87 cm = 0.87 m
4. **Calculations**
- **Period \( T \)**: Calculate \( T \) for the length used.
- **Percentage Error**: \(\% \text{error} = \frac{|T_{\text{average}} - T_{\text{standard}}|}{T_{\text{standard}}} \times 100\)
5. **Analysis**
- Does the period depend on the mass of the pendulum?
- **Conclusion**: The period is a function of \( L \) and \( g \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F549651ba-b33d-474d-abf4-48863f7a8bc4%2F7ab2a0e8-7581-4317-908e-a3af1d7beebd%2F2lhgx8x_processed.jpeg&w=3840&q=75)
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