1 / 20

Describing Periodic Motion

Describing Periodic Motion. AP Physics. Hooke’s Law. Restoring Force. The force exerted by a spring is a restoring force : it always opposes any displacement from equilibrium. Elastic Potential Energy. Work done is the area under the force vs. displacement graph

yukio
Download Presentation

Describing Periodic Motion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Describing Periodic Motion AP Physics

  2. Hooke’s Law

  3. Restoring Force • The force exerted by a spring is a restoring force: it always opposes any displacement from equilibrium

  4. Elastic Potential Energy • Work done is the area under the force vs. displacement graph • The area in this case can be found without calculus

  5. Elastic Potential Energy

  6. Periodic Motion • Any motion which repeats itself is periodic. The time it takes to compete a cycle is the period of the system. • Examples: Perfect Bouncy Ball, Pendulum, Mass on a spring, spinning object • Example: Mass on Spring

  7. Harmonic Motion • If a linear restoring force restrains the motion of an object, then the periodic motion is called simple harmonic motion • The system is called a Simple Harmonic Oscillator (SHO)

  8. Harmonic Motion • Harmonic motion can be mathematically described by a sine function.

  9. Energy Conservation • If no energy is lost, a mass on a spring will remain in motion forever. • Sacred Tenant of Physics: The total energy of the system will be conserved!

  10. Energy Conservation

  11. Example • A 1 kg. mass is attached to 25 N/m spring, stretched 10 cm from equilibrium and then released. • What is the energy stored in the system before being released? • What is the maximum velocity of the mass? • What is the velocity when the mass is at x=5 cm?

  12. Circular Motion • Simple Harmonic Motion can be compared with circular motion. • Demo • Derive the period of the system

  13. Finding the Period

  14. Period and Frequency

  15. Angular Frequency

  16. Mathematical Model

  17. Example 2 • Write an equation for the position of a 0.3 kg. mass on a 100 N/m spring that is stretched from it’s equilibrium position of 15 cm to 18 cm then released. • Find the period of the system, T • Determine the angular frequency, w • Determine the Amplitude, A • x(t) = Acos(wt)+xo.

  18. Example 3 • The position function of a 100 g. mass is given by • Determine the following:

  19. Example 3 Solutions

  20. Example 3 Solutions

More Related