PERIODIC MOTION occurs when a body
moves repeatedly over the same path in equal
intervals of time.
SIMPLE HARMONIC MOTION is linear
periodic motion in which the acceleration is
proportional to the displacement from an
equilibrium position and is directed toward the
equilibrium position.
Displacement – distance from equilibrium
Equilibrium position – midpoint of path
Amplitude – maximum displacement
Period – time for one complete cycle
Frequency – inverse of period (Hz = cycles / second)
mass–spring system
T = 2π√(m / k)
T = period in seconds
m = mass in kg
k = spring constant (N/m)
SIMPLE PENDULUMS can be examples of
simple harmonic motion.
(Mass of string must be negligible compared to the mass of the bob.)
1.Period of pendulum is independent of mass and
material of the pendulum.
2.If the arc is 15º or less, the period of the
pendulum is independent of amplitude.
3.The period of a pendulum is proportional to the
square root of its length.
4.The period of a pendulum is inversely
proportional to the square root of the
acceleration due to gravity.
SIMPLE PENDULUM
T = 2π√(l / g)
T = period in seconds
l = length of pendulum in meters
g = acceleration due to gravity (m/s2)
Daily Challenge, 9/30
A pendulum is in a spacecraft to measure the
acceleration during liftoff. Before the launch, its period
is 6.7 x 10-3 s. At a certain point during liftoff, its
frequency is 3.2 x 102 Hz. How many “g’s” are the
astronauts in the spacecraft experiencing at that point?
Lab Notebook
due Monday
Set up your slinky similarly to the set up for measuring the
spring constant. Mount a small mass to the slinky and start it
oscillating. Use the Vernier equipment to monitor both the
force acting in the spring and the motion of the mass.
Does this motion qualify as simple harmonic motion?
Be sure to determine graphically and quantitatively if the
force and acceleration are directly proportional to
displacement.
Optional addition (extra credit) to the lab:
Determine the period of the oscillation. Use it to calculate the
spring constant of the spring. Does it match your original
measurements? Explain.