1. Pendulums, Damping And Resonance

2. Pendulum
Small object (the bob) suspended from the end of a lightweight cord
Motion of pendulum very close to SHM if the amplitude of oscillation is fairly small
Restoring force is the component of the bobs weight – depends on the weight and the angle

3. Period of Pendulum T = 2√(L/ g) Period does not depend on the mass
Period does not depend on the amplitude

4. Example
Estimate the length of the pendulum in a grandfather clock that ticks once every second. B) what would the period of a clock with a 1.0m length be?

5. Example
Will a grandfather clock keep the same time everywhere? What will a clock be off if taken to the moon where gravity is 1/6 that of the earth’s?

6. Practice
A breeze sets into oscillation a lamp suspended from the ceiling. If the period is 1.0sec, what is the distance from the ceiling to the lamp?
A pendulum can be used to determine the value of g. If the period of a pendulum of length 36.90cm is found to be sec, what is the experimental value of g?

7. Damping
In any real oscillating system, the amplitude of the oscillations decreases in time until eventually stopping altogether
Effect is called damping
Generally due to air resistance or internal friction
Energy dissipated to thermal energy over time

9. Effects of Damping
Damping does alter the frequency slightly, but not enough to matter in SHM equations

10. Resonance Every vibrating system has its own natural frequency
If you try to vibrate the system at other than its natural frequency, it will bounce around but never reach any great amplitude
For example, if you push on a swing at random frequency

11. If you push on the object at the same frequency as its natural frequency, the amplitude will increase dramatically
This effect is called resonance
The natural vibrating frequency of an object is its resonant frequency

12. Breaking Glass
Music note played at same frequency as the natural vibrating frequency of a crystal glass will cause a forced vibration of the crystal
If resulting vibration is great enough in amplitude that it exceeds the glass’s elastic limit, the glass shatters