paper. It shoul a. b. our obsery ysis of your ata, On the axes to the right draw a graph of the period of a pendulum as a function of its length. LENGTH (m) Explain the shape of the graph you have drawn. Is it linear or curved? Why? Figure 11-2 C. you If you wanted to double the period of a pendulum, what change would make to its length? Explain using two points on the line you have drawn (L₁, T) and (L₂, T₂) where T₂ is 2 x T₁ and the required change in length is accurately represented. PERIOD (s)
paper. It shoul a. b. our obsery ysis of your ata, On the axes to the right draw a graph of the period of a pendulum as a function of its length. LENGTH (m) Explain the shape of the graph you have drawn. Is it linear or curved? Why? Figure 11-2 C. you If you wanted to double the period of a pendulum, what change would make to its length? Explain using two points on the line you have drawn (L₁, T) and (L₂, T₂) where T₂ is 2 x T₁ and the required change in length is accurately represented. PERIOD (s)
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![# Exploring the Period of a Pendulum
## 1. Graphing the Period as a Function of Length
### a. Drawing the Graph
On the provided axes, draw a graph representing the period of a pendulum (in seconds) as a function of its length (in meters).
### b. Analyzing the Graph's Shape
Explain the shape of the graph you have drawn. Is it linear or curved? Why?
### c. Doubling the Period
If you wanted to double the period of a pendulum, what change would you make to its length? Explain using two points on the line you have drawn \((L_1, T_1)\) and \((L_2, T_2)\) where \(T_2\) is \(2 \times T_1\), and the required change in length is accurately represented.
### Figure 11-2:
A graph is provided with the x-axis labeled "LENGTH (m)" and the y-axis labeled "PERIOD (s)."
---
## Explanation of the Graph
The period of a pendulum \(T\) is related to its length \(L\) by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
From this relationship, we can observe the following:
- When \(L\) is plotted on the x-axis and \(T\) on the y-axis, the graph will be a curve, not a straight line. This is because \(T\) increases as the square root of \(L\), leading to a parabolic shape when plotted.
- To double the period \(T\) of a pendulum, you would need to increase the length \(L\) by a factor of four. This is derived from the relationship \(T \propto \sqrt{L}\). So, if \(T_2 = 2 \times T_1\), then \((L_2 = 4 \times L_1)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a15759c-8b82-438f-9d6a-36f728df4f17%2F353e774a-8c70-4511-8e3c-02ba7980b4fc%2Fehelm1f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Exploring the Period of a Pendulum
## 1. Graphing the Period as a Function of Length
### a. Drawing the Graph
On the provided axes, draw a graph representing the period of a pendulum (in seconds) as a function of its length (in meters).
### b. Analyzing the Graph's Shape
Explain the shape of the graph you have drawn. Is it linear or curved? Why?
### c. Doubling the Period
If you wanted to double the period of a pendulum, what change would you make to its length? Explain using two points on the line you have drawn \((L_1, T_1)\) and \((L_2, T_2)\) where \(T_2\) is \(2 \times T_1\), and the required change in length is accurately represented.
### Figure 11-2:
A graph is provided with the x-axis labeled "LENGTH (m)" and the y-axis labeled "PERIOD (s)."
---
## Explanation of the Graph
The period of a pendulum \(T\) is related to its length \(L\) by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
From this relationship, we can observe the following:
- When \(L\) is plotted on the x-axis and \(T\) on the y-axis, the graph will be a curve, not a straight line. This is because \(T\) increases as the square root of \(L\), leading to a parabolic shape when plotted.
- To double the period \(T\) of a pendulum, you would need to increase the length \(L\) by a factor of four. This is derived from the relationship \(T \propto \sqrt{L}\). So, if \(T_2 = 2 \times T_1\), then \((L_2 = 4 \times L_1)\).
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