Chapter 11 Vibrations and Waves. Spring-mass system.
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Transcript of Chapter 11 Vibrations and Waves. Spring-mass system.
Chapter 11 Vibrations and Waves
Spring-mass system
kxF :Law sHooke'by given
is mass on the force thespring, aFor
Hooke’s Law
Felastic = -k x F = elastic spring force (Newtons) K = spring constant (Newtons/meter) X = length stretched or compressed
from equilibrium
Simple Harmonic Motion Repetitive or oscillating motion about an
equilibrium as a result of a restoring force that is proportional to displacement
Occurs when restoring force is proportional to displacement.
The maximum displacement from equilibrium is called the amplitude.
The frequency and period depend on the setup, and are independent of the amplitude.
Simple Harmonic Motion Continued
Frequency and Period Frequency: The number of cycles or
oscillations per unit time Measured in Hertz (Hz) 1 Hz = 1 cycle per second Period: The time for one cycle f = 1/T T = 1/f
Springs in Oscillation The period of a spring-mass system in
oscillation can be described by…
T 2m
k
Example A spring is stretched downward 5.0 cm
vertically from is relaxed position when a 500 gram mass is attached.
What is the value of its spring constant? What would its period and frequency of
oscillation be if set into simple harmonic motion?
Example A 350 g mass is attached to a spring
with 112 N/m spring constant. Find the distance the spring stretches. If the 350 g mass is taken off, how
much mass should be placed on there so that it oscillates with a frequency of 1.6 Hz?
Pendula
T 2l
g
Example How long must a pendulum clock be
made so that it keeps a time period of 2.00 seconds in a location where the acceleration due to gravity is 9.805 m/s2?
Example On the moon, a 1.500 m long pendulum
is observed to oscillate 9.87 cycles in one minute. What is the acceleration due to gravity at that location on the moon?