1. Oscillations

2. Period of Vibration Time for one oscillation depends on the stiffness of the spring Does not depend on the A SHM can be thought of similar to an object moving around a circle Time for one oscillation is the time for one revolution

3. v = 2  r/ T At max displacement r = A v o = 2  A/T T = 2  A/ v o ½ kA 2 = ½ mv o 2 A/v o =  (m/k) T = 2  (m/k)

4. 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

5. Example A 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?

6. Example A 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.

7. 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

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

9. 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?

10. 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?