Oscillations

Period of VibrationTime for one oscillation depends

on the stiffness of the springDoes not depend on the ASHM can be thought of similar to

an object moving around a circleTime for one oscillation is the

time for one revolution

v = 2r/ TAt max displacement r = A vo = 2A/T T = 2A/ vo

½ kA2 = ½ mvo2

A/vo = (m/k) T = 2(m/k)

Period of oscillation depends on m and k but not on the amplitude

Greater mass means more inertia so a slower response time and longer period

Greater k means more force required, more force causes greater acceleration and shorter period

ExampleA spider of mass 0.30g waits in its

web of negligible mass. A slight movement causes the web to vibrate with a frequency of 15 Hz. a) what is the value of k b) what frequency would you expect it to oscillate if a 0.10g insect was trapped in the web with the spider?

ExampleA large motor in a factory causes

the floor to vibrate up and down at a frequency of 10 Hz. The amplitude of the floor’s motion is 3.0 mm. Determine the maximum acceleration of the floor near the motor.

PendulumSmall 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 mass

Period 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?

ExampleWill 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?