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## Pendulums, Damping And Resonance

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**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 Pendulum**T = 2√(L/ g)**• Period does not depend on the mass • Period does not depend on the amplitude Period of Pendulum**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? Example**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 1.220 sec, what is the experimental value of g? Practice**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 Damping**Damping does alter the frequency slightly, but not enough to**matter in SHM equations Effects of Damping**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 Resonance**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**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 Breaking Glass