Physics 11: 1-6 Simple Harmonic Motion
Text Reading: Giancoli, Physics - Principles with Applications, Chapter 11: 1-6
- 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" whn 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 bouncind 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.
- Force exerted by spring:
- Frequency and period:
- Maximum potential energy of simple harmonic oscillator (A = amplitude)
- Mechanical energy at any extension x:
- Velocity at any extension x:
- Freqency and period in terms of mass and spring constant k:
- Position as a function of time:
- Period and frequency of a pendulum
Read the following weblecture before chat: Harmonic Motion
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
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- The chapter quiz is not yet due.
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