chapter 11 vibrations and waves ms. hanan. 11-2 measuring simple harmonic motion objectives identify...
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11-2 Measuring Simple harmonic 11-2 Measuring Simple harmonic MotionMotion
Objectives
• Identify the amplitude of vibration.
• Recognize the relationship between period and frequency.
• Calculate the period and frequency of an object vibrating with simple harmonic motion.
VocabularyVocabulary
• Periodic Motion• Simple Harmonic Motion• Spring-mass system• Pendulum• Vibration• Oscillation• Cycle• Period• Amplitude• Frequency• Spring Constant
Amplitude, Period, and FrequencyAmplitude, Period, and Frequency
• Amplitude is the maximum displacement from equilibrium.
• Period is the time it takes to execute a complete cycle of motion.
• Frequency is the number of cycles or vibrations per unit of time.
AmplitudeAmplitude
• Pendulum: amplitude can be measured by the angle between the pendulum’s equilibrium position and its maximum displacement.
• Mass-spring system: amplitude is the maximum amount the spring is stretched or compressed from its equilibrium position.
Period and frequency measure timePeriod and frequency measure time
• Swinging from maximum displacement on one side of equilibrium to maximum displacement on the other side and back again = one cycle
• Period (T): the time it takes for this complete cycle of motion. Units: second, s
• Frequency (f): the number of complete cycles in a unit of time. Units: 1 s-1= 1 Hz
Period of a Simple Pendulum in Simple Period of a Simple Pendulum in Simple Harmonic MotionHarmonic Motion
Depends on string length and free-fall acceleration.
L = length
Sample Problem BSample Problem B
You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and its period is 12s. How tall is the tower?
Given:
T = 12 s g = 9.81 m/s2
Unknown:L = ?
Sample Problem 12BSample Problem 12B
mL
Ls
Ls
Ls
g
L
sm
sm
sm
364
81.9144
81.9
4144
81.9212
2 T
2
2
22
2
2
2
AssignmentsAssignments
• Class-work: Practice B , page 379, questions 1, 2, 3, and 4.
• Homework: Section review on page 381 questions 1 and 2
Review; Page 397: # 19 and 20
Sample Problem CSample Problem C
The body of a 1275 kg car is supported on a frame by four springs. Two people riding in the car have a combined mass of 153 kg. when driven over a pothole in the road, the frame vibrates with a period of 0.840 s. for the first few seconds, the vibration approximates simple harmonic motion. Find the spring constant of a single spring.
Given:
T = 0.840 sUnknown:
k = ?
357kg
4153kg1275kg
m