REAL DATA ms= SPRING MASS msEFF = ms/3 MASS OF HANGER AND ADDED WEIGHTS m IN EQUATION 1 T 2TT We are now in the position to COMPARE after finding the theoretical period given by formula (1) for T: EQUATION (1): m 174.49 0.1744 kg 58.13g ~ 0.05813 kg K ≈ 300g = 0.300 kg 0.300+ M₂/8 = 0.35813 Kg
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.
![### Educational Resource: Spring Mass System Analysis
#### Real Data:
- **m<sub>s</sub> = Spring Mass**
- 174.4 g ≈ 0.1744 kg
- **m<sub>sEFF</sub> = m<sub>s</sub>/3**
- 58.13 g ≈ 0.05813 kg
- **Mass of Hanger and Added Weights**
- 300 g = 0.300 kg
- **m in Equation 1:**
- 0.300 + m<sub>s</sub>/3 = 0.35813 kg
#### Analysis:
We are now in the position to **COMPARE** after finding the theoretical period given by formula (1) for T:
#### Equation (1):
\[ T = 2\pi \sqrt{\frac{m}{K}} \]
This formula is used to calculate the theoretical period \( T \) of a spring-mass system, where:
- \( m \) is the effective mass.
- \( K \) is the spring constant.
- \( \pi \) is a constant approximately equal to 3.14159.
Understanding this equation helps in analyzing oscillatory systems and comparing theoretical and experimental results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdab67aeb-c4d9-43f7-88d0-dfd6e7af2d5d%2Ff5e7f686-a949-426d-a10d-0be015115cc0%2Fuc30603_processed.jpeg&w=3840&q=75)
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