Homework Help is Here – Start Your Trial Now!
Science
Physics
2. A simple pendulum consists of a point mass m suspended by a massless string with length. The point mass will oscillate back and forth along a circular are with radius . This is an example of a system that approximately undergoes simple harmonic motion under certain conditions. m a) Determine the angular acceleration of the point mass, which should lead you to a differential equation for the angle 0. b) Now suppose the angle is very small. If the angle is small, sin (if you look at a graph of sin 0, for small , you should see that sin is approximately linear). Using this approximation, show that your answer to part a) leads to simple harmonic motion. Find the period, frequency, and angular frequency of the oscillations. c) For this part, suppose = 0.5 m, m = 2 kg, and at t=0 the mass is at rest at an angle = -0.1 rad (note: a negative angle mean's the mass is to the left of the vertical). What is as a function of time? d) Assuming the oscillations are small, what physical properties affect the period of the system? If you increase the mass m, what happens to the period? If you increase or decrease the length of the string, what happens to the period? What if the pendulum was near the surface of the moon instead of the earth, what would happen to the period? Make sure

2. A simple pendulum consists of a point mass m suspended by a massless string with length. The point mass will oscillate back and forth along a circular are with radius . This is an example of a system that approximately undergoes simple harmonic motion under certain conditions. m a) Determine the angular acceleration of the point mass, which should lead you to a differential equation for the angle 0. b) Now suppose the angle is very small. If the angle is small, sin (if you look at a graph of sin 0, for small , you should see that sin is approximately linear). Using this approximation, show that your answer to part a) leads to simple harmonic motion. Find the period, frequency, and angular frequency of the oscillations. c) For this part, suppose = 0.5 m, m = 2 kg, and at t=0 the mass is at rest at an angle = -0.1 rad (note: a negative angle mean's the mass is to the left of the vertical). What is as a function of time? d) Assuming the oscillations are small, what physical properties affect the period of the system? If you increase the mass m, what happens to the period? If you increase or decrease the length of the string, what happens to the period? What if the pendulum was near the surface of the moon instead of the earth, what would happen to the period? Make sure

College Physics
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)...
See similar textbooks
icon
Related questions
icon
Concept explainers
Topic Video
Question
2. A simple pendulum consists of a point mass m suspended by a massless string with length. The point mass will oscillate back and forth along a circular are with radius . This is an example of a system that approximately undergoes simple harmonic motion under certain conditions. m a) Determine the angular acceleration of the point mass, which should lead you to a differential equation for the angle 0. b) Now suppose the angle is very small. If the angle is small, sin ≈ 0 (if you look at a graph of sin 0, for small 0, you should see that sin is approximately linear). Using this approximation, show that your answer to part a) leads to simple harmonic motion. Find the period, frequency, and angular frequency of the oscillations. c) For this part, suppose l = 0.5 m, m = 2 kg, and at t=0 the mass is at rest at an angle = -0.1 rad (note: a negative angle mean's the mass is to the left of the vertical). What is as a function of time? d) Assuming the oscillations are small, what physical properties affect the period of the system? If you increase the mass m, what happens to the period? If you increase or decrease the length of the string, what happens to the period? What if the pendulum was near the surface of the moon instead of the earth, what would happen to the period? Make sure to briefly explain the physical reasoning behind your conclusions. Don't just look at your equation for the period, think about what is happening physically.
Transcribed Image Text:2. A simple pendulum consists of a point mass m suspended by a massless string with length. The point mass will oscillate back and forth along a circular are with radius . This is an example of a system that approximately undergoes simple harmonic motion under certain conditions. m a) Determine the angular acceleration of the point mass, which should lead you to a differential equation for the angle 0. b) Now suppose the angle is very small. If the angle is small, sin ≈ 0 (if you look at a graph of sin 0, for small 0, you should see that sin is approximately linear). Using this approximation, show that your answer to part a) leads to simple harmonic motion. Find the period, frequency, and angular frequency of the oscillations. c) For this part, suppose l = 0.5 m, m = 2 kg, and at t=0 the mass is at rest at an angle = -0.1 rad (note: a negative angle mean's the mass is to the left of the vertical). What is as a function of time? d) Assuming the oscillations are small, what physical properties affect the period of the system? If you increase the mass m, what happens to the period? If you increase or decrease the length of the string, what happens to the period? What if the pendulum was near the surface of the moon instead of the earth, what would happen to the period? Make sure to briefly explain the physical reasoning behind your conclusions. Don't just look at your equation for the period, think about what is happening physically.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 10 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Simple Harmonic Motion
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS