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The image you uploaded appears to be a worksheet related to physics, specifically focusing on the concepts of simple harmonic motion (SHM) and oscillations. The task involves analyzing data from experiments or simulations and applying formulas to calculate various physical quantities such as angular frequency, period, amplitude, and displacement.

Step-by-Step Solution and Explanation

#### 1. Understanding the Problem
The worksheet provides:
- A table with experimental data for different oscillatory systems.
- Formulas for calculating angular frequency (\(\omega\)), period (\(T\)), amplitude (\(A\)), and displacement (\(x\)).
- Instructions to fill in missing values based on the given data.

#### 2. Key Formulas
The following formulas are relevant:
1. Angular Frequency (\(\omega\)):
\[
\omega = 2\pi f
\]
where \(f\) is the frequency in Hz.

2. Period (\(T\)):
\[
T = \frac{1}{f}
\]
or equivalently,
\[
T = \frac{2\pi}{\omega}
\]

3. Amplitude (\(A\)):
- The amplitude is the maximum displacement from the equilibrium position. It is typically given or can be measured directly from the data.

4. Displacement (\(x\)):
For simple harmonic motion, the displacement as a function of time is given by:
\[
x(t) = A \cos(\omega t + \phi)
\]
where:
- \(A\) is the amplitude,
- \(\omega\) is the angular frequency,
- \(t\) is the time,
- \(\phi\) is the phase constant.

#### 3. Solving the Worksheet
Let's break down the solution step by step:

##### Part 1: Filling in the Table
The table likely contains columns for:
- Frequency (\(f\)),
- Angular frequency (\(\omega\)),
- Period (\(T\)),
- Amplitude (\(A\)),
- Displacement (\(x\)) at specific times.

We need to use the given data and formulas to fill in the missing values.

##### Example Calculation
Suppose the table has the following data for one row:
- Frequency (\(f\)): 2 Hz
- Amplitude (\(A\)): 5 cm
- Time (\(t\)): 0.5 s
- Phase constant (\(\phi\)): 0 (assuming no phase shift)

1. Calculate Angular Frequency (\(\omega\)):
\[
\omega = 2\pi f = 2\pi \times 2 = 4\pi \, \text{rad/s}
\]

2. Calculate Period (\(T\)):
\[
T = \frac{1}{f} = \frac{1}{2} = 0.5 \, \text{s}
\]

3. Calculate Displacement (\(x\)) at \(t = 0.5 \, \text{s}\):
Using the formula \(x(t) = A \cos(\omega t + \phi)\):
\[
x(0.5) = 5 \cos(4\pi \times 0.5 + 0) = 5 \cos(2\pi) = 5 \cos(0) = 5 \, \text{cm}
\]

##### Repeat for Other Rows
Repeat the above calculations for each row in the table, using the given data for frequency, amplitude, time, and phase constant.

##### Part 2: Graphical Analysis
The worksheet may also ask you to:
- Plot the displacement (\(x\)) versus time (\(t\)) graph.
- Identify the amplitude, period, and frequency from the graph.

- Amplitude: The maximum value of \(x\) on the graph.
- Period: The time taken for one complete cycle.
- Frequency: The reciprocal of the period (\(f = \frac{1}{T}\)).

##### Part 3: Answering Questions
Answer the questions based on your calculations and observations:
- Explain the relationship between frequency and period.
- Discuss how changing the amplitude affects the motion.
- Interpret the phase constant (\(\phi\)) and its effect on the motion.

#### 4. Final Answer
After completing all calculations and filling in the table, the final answer will be the completed table with all missing values filled in, along with any required graphs and explanations.

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Boxed Final Answer

\[
\boxed{\text{See detailed steps above for calculations and explanations.}}
\]

If you provide specific rows or data from the table, I can perform the calculations for those rows explicitly. Let me know if you need further clarification!