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?