Oscillatory motion. Simple harmonic motion. The simple pendulum. Damped harmonic oscillations. (Lecture 1)
Содержание
- 2. Lecture 1 Oscillatory motion. Simple harmonic motion. The simple pendulum. Damped harmonic oscillations. Driven harmonic oscillations.
- 3. Harmonic Motion of Object with Spring A block attached to a spring moving on a frictionless
- 4. x is displacement from equilibrium position. Restoring force is given by Hook’s law: Then we can
- 5. Simple Harmonic Motion An object moves with simple harmonic motion whenever its acceleration is proportional to
- 6. Mathematical Representation of Simple Harmonic Motion So the equation for harmonic motion is: We can denote
- 7. A=const is the amplitude of the motion ω=const is the angular frequency of the motion φ=const
- 8. The inverse of the period is the frequency f of the oscillations:
- 9. Then the velocity and the acceleration of a body in simple harmonic motion are:
- 10. Position vs time Velocity vs time At any specified time the velocity is 90° out of
- 11. Energy of the Simple Harmonic Oscillator Assuming that: no friction the spring is massless Then the
- 12. The total mechanical energy of simple harmonic oscillator is: That is, the total mechanical energy of
- 13. Simple Pendulum Simple pendulum consists of a particle-like bob of mass m suspended by a light
- 15. The period and frequency of a simple pendulum depend only on the length of the string
- 16. Physical Pendulum If a hanging object oscillates about a fixed axis that does not pass through
- 17. Applying the rotational form of the second Newton’s law: The solution is: The period is
- 18. Damped Harmonic Oscillations In many real systems, nonconservative forces, such as friction, retard the motion. Consequently,
- 19. The solution for small b is When the retarding force is small, the oscillatory character of
- 20. The angular frequency can be expressed through ω0=(k/m)1/2 – the natural frequency of the system (the
- 21. underdamped oscillator: Rmax=bVmax critically damped oscillator: when b has critical value bc= 2mω0 . System does
- 22. Driven Harmonic Oscillations A driven (or forced) oscillator is a damped oscillator under the influence of
- 23. The forced oscillator vibrates at the frequency of the driving force The amplitude of the oscillator
- 24. Resonance So resonance happens when the driving force frequency is close to the natural frequency of
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