Pendulums, Damping And Resonance

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

Period of Pendulum

T = 2√(L/ g)

Period does not depend on the massPeriod does not depend on the amplitude

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?

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?

Practice

1) 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?

2) 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 1.220 sec, what is the experimental value of g?

Damping

In any real oscillating system, the amplitude of the oscillations decreases in time until eventually stopping altogether

Effect is called dampingGenerally due to air resistance or internal

frictionEnergy dissipated to thermal energy over

time

Effects of Damping

Damping does alter the frequency slightly, but not enough to matter in SHM equations

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

If you push on the object at the same frequency as its natural frequency, the amplitude will increase dramatically

This effect is called resonanceThe natural vibrating frequency of an

object is its resonant frequency

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