Physics 11: 1-6 Simple Harmonic Motion

Homework

Reading Preparation
Key Equations
WebLecture
Study Activity
Chat Preparation Activities
Chapter Quiz
Lab Work

Reading Preparation

Text Reading: Giancoli, Physics - Principles with Applications, Chapter 11: 1-6

Study Points

11.1: Simple harmonic motion is motion that repeats exactly within a given period of time T. The frequency is defined as f = 1/T. The amplitude is the amount of displacement of the system from "rest" when it is unstressed. Simple harmonic motion can be described using trigonometric functions that relate the amount of displacement to time.
11.2: Another way to look at a simple harmonic oscillator such as a spring is as a system which converts PE to KE and back. As displacement decreases (PE goes down), velocity increases (KE goes up). KE is maximum when displacement is 0, and KE is minimum when displacement is maximum.
11.3: The components of repeated motions such as springs bouncing and pendula swinging can be expressed in trigonometric terms, where x = A cos ωt = A sin 2πt/T
11.4: We can now analyze pendular motion, noting that for small displacements, x = Lθ and T = 2π sqrt(L/g). NOTE THAT the period does NOT depend on the mass of the bob, but only on the length of the string.
11.5: Damped harmonic motion occurs when friction in the system slows the swing down iteratively (some amount each swing). Damping can change the behavior of a normally periodic system to the point where standard periodic analysis is impossible.
11.6: An external force applied to a periodic system can force the system to change periods. However, if the external force matches the natural period of the system, we have a resonance situation. The external force "pumps" the system, increasing energy and amplitude.

Key Equations

Force exerted by spring: $F = - kx$
Frequency and period: $f = \frac{1}{T} \Rightarrow T = \frac{1}{f}$
Maximum potential energy of simple harmonic oscillator (A = amplitude) $E = ½ k A^{2}$
Mechanical energy at any extension x: $½ m v^{2} + ½ k x^{2} = ½ k A^{2}$
Velocity at any extension x: $v^{2} = \frac{k}{m} (A^{2} - x^{2}) \Rightarrow v_{\max} = \sqrt{\frac{k}{m}} A$
Frequency and period in terms of mass and spring constant k: $T = 2 π \sqrt{\frac{m}{k}} \Rightarrow f = \frac{1}{T} = \frac{1}{2 π} \sqrt{\frac{k}{m}}$
Position as a function of time: $x = A \cos θ = A \cos ω t = A \cos (2 π ft) = A \cos (\frac{2 π t}{T})$
Period and frequency of a pendulum $T = 2 π \sqrt{\frac{l}{g}} \Rightarrow f = \frac{1}{T} = \frac{1}{2 π} \sqrt{\frac{g}{l}}$

Web Lecture

Read the following weblecture before chat: Harmonic Motion

Study Activity

Use the simulation below to explore pendulum motion.

Click on Intro to open the pendulum simulation. Displace the pendulum by dragging it to one side (note your release angle) and releasing it. Use the stopwatch to determine the period. Does the period change if you displace the pendulum to different heights?
Reset the simulation to initial conditions by clicking on the orange button with the circle in the lower right. Now change the length of the pendulum, and restart the simulation. Displace the pendulum to the same release angle you used before and release it. Does the period change if you change the length of the pendulum?
Reset the simulation to initial conditions by clicking on the orange button with the circle in the lower right. Now change the mass of the pendulum, and restart the simulation. Displace the pendulum to the same release angle you used before and release it. Does the period change if you change the length of the pendulum?
Add that the second pendulum, and compare periods and motions simultaneously.
Explore the energy simulation and note how kinetic and potential energy change as components of the total energy for the pendulum.

Physics simulation Java Applets are the product of the PHET Interactive Simulations project at the University of Colorado, Boulder.

Chat Preparation Activities

Forum question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

Chapter Quiz

The chapter quiz is not yet due.

Lab Work

If you want lab credit for this course, you must complete at least 18 labs; you may complete more if you are preparing for the AP exam.. One or more lab exercises are posted for each chapter as part of the homework assignment. We will be reviewing lab work at regular intervals, so do not get behind!

Lab Instructions: Spring Oscillation

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Physics

Chapter 11: 1-6 Assignment