Damped & Driven Oscillations Resonance

1. Damped & Driven Oscillations Resonance

2. So far we have talked about systems that if disturbed from equilibrium, they would oscillate indefinitely around the equilibrium position. • But normally, that doesn’t happen. • Normally, systems return to equilibrium.

3. Damped Oscillations Ch 13.6 • Oscillation with friction • In the real world, there are dissipative forces such as friction . Such a dissipative force will decrease the amplitude of the oscillation • Friction reduces the mechanical energy of the system as time passes, and the motion is said to be damped.

4. F = -bv • With most damped oscillations, the oscillating mass looses its energy to a force that is proportional to the speed of the object and opposite in direction b = damping constant “b” is a measure of the strength of the damping force (units: kg/s)

5. Types of Damping • Underdamped– vibrating motion is preserved, but amplitude of vibration decreases with time and motion ultimately ceases. • Critically damped • Overdamped

6. Types of Damping • Underdamped • Critically Damped – Object returns to equilibrium in the shortest amount of time, never overshooting equilibrium. • Overdamped .

7. Types of Damping • Underdamped • Critically Damped • Overdamped – Object returns to equilibrium without ever passing through the equilibrium position, but the time required to reach equilibrium is greater than in critical damping.

8. Automobile shock absorbers make a car more comfortable to ride in. When a car goes over a speed bump, the car body of the car will oscillate a few times about the equilibrium position before returning to its fixed position. What type of damping is this? • Underdamped • Critically damped • Overdamped

9. Driven Oscillation • To prevent a system from loosing all its energy to damping, energy must be continually added to the system. This is called a driven oscillation. • Moving your hand can cause a driven oscillation in a simple pendulum, but not all movement will work. • If you move your hand too slow, the mass follows your hand. • If you move your hand too fast, then only small amplitude oscillations occur. • If you move your hand just right, the mass can swing indefinitely.

10. What is just right? Natural Frequency • The pendulum would swing on its own with a given frequency. • This is called the natural frequency. • If the movement of your hand matches the natural frequency of the pendulum, then your hand will be adding energy at just the right places and this will lead to a driven oscillation.

11. Resonance 14.8, 14.9 & 14.10 • When energy is added in time with the natural frequency of an object, a little increase in energy will lead to a large increase in amplitude. • This is called Resonance. • Examples: Blowing over a bottle. • Swinging/pushing someone on a swing. • Tacoma Narrows Bridge