C Y C L E
V
IB
R
E
TC
C
S
OS
LK
Y
A
L
IB
R
A
KX
G
S
ES
PH
O
A
S H A K E
V I B R A T E
V
IB
R
A
TE
U
S
ES
ND
O
A
Describe the bobblehead doll’s head.
Periodic Frequency
Oscillating Period
Damping Time
Position Speed
Cycle Displacement
Maximum Amplitude
Minimum Force
Inter...
A vibrating object is wiggling
about a fixed position.
A motion that is regular and
repeating is referred to as
a periodic...
Simple Harmonic Motion
• Definition
– Simple harmonic motion occurs when
the force F acting on an object is
directly propo...
• Descriptive terms
–The amplitude A is the maximum
displacement from the equilibrium
position.
–The period T is the time ...
The Formulas
Parameter Unit Definition Equation
Period
(T)
s
(Second)
Time to complete one
cycle/vibration
1
f
Frequency
(...
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
4...
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 New...
Set 1: Simple Pendulum
1. A pendulum makes 35 complete oscillations in 12 s. (a)
What is its period? (b) What is its frequ...
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...
2. Perpetually disturbed by the habit of the
backyard squirrels to raid his bird feeders, Mr.
H decides to use a little ph...
3. Referring to the previous question. If Mr. H
wishes to have his bird feeder (and attached
squirrel) vibrate with the hi...
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
Simple harmonic motion
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Simple harmonic motion

  1. 1. C Y C L E V IB R E TC C S OS LK Y A
  2. 2. L IB R A KX G S ES PH O A S H A K E
  3. 3. V I B R A T E V IB R A TE U S ES ND O A
  4. 4. Describe the bobblehead doll’s head.
  5. 5. Periodic Frequency Oscillating Period Damping Time Position Speed Cycle Displacement Maximum Amplitude Minimum Force Interval Equilibrium
  6. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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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