6-Simple Harmonic Motion

Slideshow: SHM and oscillations notes

Textbook: Chapter 19 in Mastering Physics (get online code for registration on about page of google classroom)

Objectives:

  • Explain how restoring forces can cause oscillations; how linear restoring forces cause simple harmonic motion
    • predict, plan data collection, analyze data and explain oscillatory motion
  • A system with internal structure can have internal energy (aka potential energy). Changes in a system's structure can change the energy
  • Spring mass oscillators:
    • T increases with m and decreases with k (spring stiffness)
    • Calculate force & acceleration for any location along an object oscillating along a spring. (Especially consider minima, maxima and zeroes for position, velocity and acceleration)
    • mass-spring systems convert kinetic energy into elastic potential and vice versa based on energy conservation.
  • Simple pendulums:
    • T increases with L and decreases with the g (magnitude of gravitational field).
    • Potential energy exists within a system if the objects have conservative forces (springs & gravity)
    • Pendulums convert kinetic energy into gravitational potential energy and vice versa based on energy conservation.

Equations:

And the restoring force of a simple harmonic oscillator can be found using

|Fs|=k|x|

Common Misconceptions: (these statements all have flaws)

    • The period of oscillation depends on the amplitude.
    • The heavier a pendulum bob, the shorter its period.
    • All pendulum motion is perfect simple harmonic motion, for any initial angle.
    • Harmonic oscillators go forever.
    • A pendulum accelerates through lowest point of its swing.
    • Amplitude of oscillations is measured peak-to-peak.
    • The acceleration is zero at the end points of the motion of a pendulum.
    • The restoring force is constant at all points in the oscillation.