# Exploring the Period of a Pendulum## 1. Graphing the Period as a Function of Length### a. Drawing the GraphOn 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 ShapeExplain the shape of the graph you have drawn. Is it linear or curved? Why?### c. Doubling the PeriodIf 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 GraphThe 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 \((L_2 = 4 \times L_1)\).

Solution:Acceleration of mass m = -d2xdt2Since, x = Lθa =-Ld2θdt2Now, we know that tangential force…

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)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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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