1 / 22

Do now!

Do now!. Can you hand your SHM questions in please?. This lesson. Considering energy changes during SHM Applying E k = ½mω 2 (x o 2 – x 2 ) E T = ½mω 2 x o 2 E p = ½mω 2 x 2 where ω = 2πf = 2π/T. S.H.M. Where is the kinetic energy maxiumum?

christopher-anania
Download Presentation

Do now!

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. Do now! Can you hand your SHM questions in please?

  2. This lesson • Considering energy changes during SHM • Applying Ek = ½mω2(xo2 – x2) ET = ½mω2xo2 Ep = ½mω2x2 where ω = 2πf = 2π/T

  3. S.H.M. Where is the kinetic energy maxiumum? Where is the potential energy maximum?

  4. It can be shown that…. Ek = ½mω2(xo2 – x2) ET = ½mω2xo2 Ep = ½mω2x2 where ω = 2πf = 2π/T

  5. Example A mass-spring system oscillates with an amplitude of 3.5cm. If the force constant of the spring of 250Nm-1 and the mass is 0.5kg, determine(a) the total energy of the system,(b) the maximum speed of the mass (c) the maximum acceleration

  6. A mass-spring system oscillates with an amplitude of 3.5cm. If the force constant of the spring of 250Nm-1 and the mass is 0.5kg, determine(a) the total energy of the system,(b) the maximum speed of the mass(c) the maximum acceleration (a) We have m = 0.5kg, xo = 0.035m, k = 250N/m • = √k/m = √500= 22.36 rad.s-1 ET = ½mω2xo2= ½(0.5)(22.36)2(0.035)2 =0.153J.

  7. A mass-spring system oscillates with an amplitude of 3.5cm.  If the force constant of the spring of 250Nm-1 and the mass is 0.5kg, determine(a) the total energy of the system,(b) the maximum speed of the mass(c) the maximum acceleration (b) Maximum speed when x = 0(Ek = max) At this point, the total energy is all kinetic Ek = 0.153 J = ½mv2 v2 = (2 x 0.153)/0.5 = 0.612 v = 0.78m.s-1

  8. A mass-spring system oscillates with an amplitude of 3.5cm.  If the force constant of the spring of 250Nm-1 and the mass is 0.5kg, determine(a) the total energy of the system,(b) the maximum speed of the mass(c) the maximum acceleration (c) Maximum acceleration (force) when x = xo F = -kx = -250 x 0.035 = 8.75 N a = F/m = 8.75/0.5 = 17.5 m.s-2

  9. Last lesson • Considering energy changes during SHM • Applying Ek = ½mω2(xo2 – x2) ET = ½mω2xo2 Ep = ½mω2x2 where ω = 2πf = 2π/T

  10. This lesson • Know what is meant by damping • Describe damped oscillations • Know what is meant by natural frequency and forced oscillation • Describe graphically forced oscillations near the natural frequency • Know what is meant by resonance and describe examples

  11. Damping

  12. Damping In most real oscillating systems energy is lost through friction. The amplitude of oscillations gradually decreases until they reach zero. This is called damping

  13. Heavy Damping Sometimes the damping is so large that the motion no longer resembles SHM

  14. Overdamped The system takes a long time to reach equilibrium

  15. Underdamped The system makes several oscillations before coming to rest

  16. Critical damping Equilibrium is reached in the quickest time

  17. YouTube - Tacoma Bridge Disaster Forced vibrations - resonance

  18. Natural frequency All objects have a natural frequency that they prefer to vibrate at.

  19. Forced vibrations If a force is applied at a different frequency to the natural frequency we get forced vibrations

  20. Resonance If the frequency of the external force is equal to the natural frequency we get resonance YouTube - Ground Resonance - Side View YouTube - breaking a wine glass using resonance

  21. Let’s try some more questions!

More Related