How to solve %diff in t just for on secti
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How to solve %diff in t just for on secti
![### Determination of the Period and Frequency of Simple Harmonic Motion
Table #2 illustrates the determination of the period and frequency of simple harmonic motion through experimental assessment and theoretical calculation. Below is the data and subsequent measurements:
| \( M_{sw} \) (g) | \( M_T \) (g) | \( M_T \) (kg) | \( t_{10} \) (s) | \( T_{exp} \) (s) | \( T_{th} = 2 \pi \sqrt{\frac{M_T}{K}} \) (s) | \(\% \text {dif in } T \) |
|:---------------:|:-------------:|:--------------:|:---------------:|:----------------:|:---------------------------------------------------:|:------------------------:|
| 200 | 290 | 0.29 | 4.16 | 0.416 | 0.6007064 | |
| 220 | 296 | 0.296 | 4.56 | 0.456 | 2.00703299 | |
| 240 | 290 | 0.290 | 5.88 | 0.588 | 2.0070899 | |
Frequency when \( M_{sw} = 200 \) g:
\[ f_{exp} = \frac{1}{T_{exp}} \]
**Note:**
\[
\begin{aligned}
M_H &: \text{Mass of the weight hanger} \\
M_{sw} &: \text{Mass of added slotted weights} \\
M_T &: \text{Total Mass} \\
T_{exp} &: \text{Experimental period} \\
t_{10} &: \text{Time for 10 oscillations} \\
T_{th} &: \text{Theoretical period} \\
f_{exp} &: \text{Experimental frequency} \\
\pi & = 3.14
\end{aligned}
\]
#### Questions:
1. How does the period change with increasing mass?
This data and analysis are crucial for understanding the dynamics of simple harmonic motion and validating theoretical predictions with experimental results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb15e654-30a5-46a4-8934-d26e13081e17%2F8c14e162-87a7-4b86-92bb-3aab5b799356%2Fvu6nzv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determination of the Period and Frequency of Simple Harmonic Motion
Table #2 illustrates the determination of the period and frequency of simple harmonic motion through experimental assessment and theoretical calculation. Below is the data and subsequent measurements:
| \( M_{sw} \) (g) | \( M_T \) (g) | \( M_T \) (kg) | \( t_{10} \) (s) | \( T_{exp} \) (s) | \( T_{th} = 2 \pi \sqrt{\frac{M_T}{K}} \) (s) | \(\% \text {dif in } T \) |
|:---------------:|:-------------:|:--------------:|:---------------:|:----------------:|:---------------------------------------------------:|:------------------------:|
| 200 | 290 | 0.29 | 4.16 | 0.416 | 0.6007064 | |
| 220 | 296 | 0.296 | 4.56 | 0.456 | 2.00703299 | |
| 240 | 290 | 0.290 | 5.88 | 0.588 | 2.0070899 | |
Frequency when \( M_{sw} = 200 \) g:
\[ f_{exp} = \frac{1}{T_{exp}} \]
**Note:**
\[
\begin{aligned}
M_H &: \text{Mass of the weight hanger} \\
M_{sw} &: \text{Mass of added slotted weights} \\
M_T &: \text{Total Mass} \\
T_{exp} &: \text{Experimental period} \\
t_{10} &: \text{Time for 10 oscillations} \\
T_{th} &: \text{Theoretical period} \\
f_{exp} &: \text{Experimental frequency} \\
\pi & = 3.14
\end{aligned}
\]
#### Questions:
1. How does the period change with increasing mass?
This data and analysis are crucial for understanding the dynamics of simple harmonic motion and validating theoretical predictions with experimental results.
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