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- 1. C Y C L E V IB R E TC C S OS LK Y A
- 2. L IB R A KX G S ES PH O A S H A K E
- 3. V I B R A T E V IB R A TE U S ES ND O A
- 4. Describe the bobblehead doll’s head.
- 5. Periodic Frequency Oscillating Period Damping Time Position Speed Cycle Displacement Maximum Amplitude Minimum Force Interval Equilibrium
- 6. A vibrating object is wiggling about a fixed position. A motion that is regular and repeating is referred to as a periodic motion.
- 7. Simple Harmonic Motion • Definition – Simple harmonic motion occurs when the force F acting on an object is directly proportional to the displacement x of the object, but in the opposite direction. – Mathematical statement F = -kx – The force is called a restoring force because it always acts on the object to return it to its equilibrium position.
- 8. • Descriptive terms –The amplitude A is the maximum displacement from the equilibrium position. –The period T is the time for one complete oscillation. After time T the motion repeats itself. In general x(t) = x (t + T) –The frequency f is the number of oscillations per second. The frequency equals the reciprocal of the period. f = 1/T. –Although simple harmonic motion is not motion in a circle, it is convenient to use angular frequency by defining ω = 2πf = 2π/T.
- 9. The Formulas Parameter Unit Definition Equation Period (T) s (Second) Time to complete one cycle/vibration 1 f Frequency (f) Hz (Hertz) Number of cycles per unit time 1 ω T 2π Restoring Force (F) N (newton) Force that causes the mass to return to its equilibrium position F = -kx Angular Velocity (ω) m/s (meter/se cond) Rate of angular displacement per unit time k m T = f = = ω = T = 2π L g
- 10. Cycle Letters Times at Beginning and End of Cycle (in seconds) Cycle Time (in seconds) 1st A to E 0.0 to 2.3 2.3 2nd 3rd 4th 5th 6th Mass – Spring Sinusoidal Graph
- 11. Exercise 1. A force of 16 N is required to stretch a spring a distance of 40 cm from its rest position. What force (in Newtons) is required to stretch the same spring … a. … twice the distance? b. … three times the distance? c. … one-half the distance? 32 N 48 N 8 N
- 12. Set 1: Simple Pendulum 1. A pendulum makes 35 complete oscillations in 12 s. (a) What is its period? (b) What is its frequency? 2. (a) A pendulum is 3.500 m long. What is its period at the North Pole where g = 9.832 m/s2? (b) In Java (g=9.782 m/s2?) 3. A pendulum has a frequency of 5.50 Hz on earth at a point where g = 9.80 m/s2. What would be its frequency in Jupiter where the acceleration due to gravity is 2.54 times than on earth? 4. A simple pendulum has a period of 2.4 s at a location where the acceleration due to gravity is 9.7 m/s2. What is the length of the pendulum?
- 13. Homework 1. A pendulum extend from the roof of a building almost to the floor. If the pendulum’s period is 8.5 s, how tall is the buliding? 2. What is the period of a 1.00-m-long pendulum is a space craft orbiting at 6.70 x 106 m above the earth’s surface? Use the formula: g = G·me/d2 where: me=5.96 x 1024kg, G = 6.67 x01-11N m2/kg2 and d = 6.37 x 106 m)
- 14. 2. Perpetually disturbed by the habit of the backyard squirrels to raid his bird feeders, Mr. H decides to use a little physics for better living. His current plot involves equipping his bird feeder with a spring system that stretches and oscillates when the mass of a squirrel lands on the feeder. He wishes to have the highest amplitude of vibration that is possible. Should he use a spring with a large spring constant or a small spring constant?
- 15. 3. Referring to the previous question. If Mr. H wishes to have his bird feeder (and attached squirrel) vibrate with the highest possible frequency, should he use a spring with a large spring constant or a small spring constant?

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