1 / 10

Harmonic Motion ( IV )

Harmonic Motion ( IV ). Energy of a simple harmonic oscillator. Energy of a SHO. Recall: E Tot = K + U = 1/2mv 2 + 1/2kx 2 for a spring. But we know that: x=A cos( ω t+ φ ) v=-A ω sin( ω t+ φ ). M. Energy in SHM.

cseeley
Télécharger la présentation

Harmonic Motion ( IV )

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. Harmonic Motion (IV) • Energy of a simple harmonic oscillator Physics 1D03 - Lecture 34

  2. Energy of a SHO Recall: ETot = K + U = 1/2mv2 + 1/2kx2 for a spring. But we know that: x=A cos(ωt+φ) v=-A ω sin(ωt+φ) Physics 1D03 - Lecture 34

  3. M Energy in SHM Look again at the block & spring Hence: ETot = ½kA2 We could also write E = K+U = ½ m(vmax )2 Physics 1D03 - Lecture 34

  4. Concept Quiz Suppose you double the amplitude of the motion, what happens to the maximum speed ? • Doubles • 4 x Larger • Doesn’t change Physics 1D03 - Lecture 34

  5. Concept Quiz • Suppose you double the amplitude of the motion, what • happens to the maximum acceleration? • Doubles • 4 x Larger • Doesn’t change Physics 1D03 - Lecture 34

  6. Concept Quiz • Suppose you double the amplitude of the motion, what • happens to the the total energy? • Doubles • 4 x Larger • Doesn’t change Physics 1D03 - Lecture 34

  7. Energy Since we know the total energy of a SHM, we can calculate the or displacement velocity at any point in time: ETot=1/2kA2 = K+U = 1/2mv2 + 1/2kx2 So, if x=0, all E is in kinetic, and v is at max if x=A, all E is in potential, and v is zero Physics 1D03 - Lecture 34

  8. Example A 100g block is 5cm from the equilibrium position moving at 1.5m/s. a) What is the total energy of the system ? b) What is the amplitude of the oscillations ? Physics 1D03 - Lecture 34

  9. Example A 500g block on a spring is pulled 20cm and released. The motion has a period of 0.8s. What is the velocity when the block is 15.4cm from the equilibrium ? Physics 1D03 - Lecture 34

  10. Example A 1.0kg block is attached to a spring with k=16N/m. While the block is at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 40cm/s. • what is the amplitude of the subsequent oscillations ? • what is the block’s speed at the point where x=A/2 ? Physics 1D03 - Lecture 34

More Related