Oscillations
This lab will be assessed on data collection and processing only.
Introduction:
A system will undergo periodic motion provided a restoring force acts
in a direction opposite to displacement towards a stable equilibrium point.
When the restoring force is directly proportional to the displacement then
the system undergoes simple harmonic motion (SHM). The resulting equation
of motion is sinusoidal and it can be shown that the period of motion is
independent of the amplitude. In this lab you will investigate an oscillating
spring system consisting of a number of different springs connected together.
How does the period change as you increase the number of springs?
Procedure:
First determine the spring constant k of each of the three similar
springs you are given by applying four or five different weights to the
end of each
spring and measuring the extension (plot a graph of weight vs extension
and find the slope).
Next attach a mass m to one of the springs and suspend the system from the ceiling. Set the system into oscillatory motion and measure the period T. Using the equation for the period of motion T,
,
find the spring constant k and compare this measurement with your earlier result. Do the two values agree within experimental error?
Next attach two springs together with the mass at one end and set this system into oscillatory motion. Measure the period and use the equation above to find the effective spring constant for the combined system.
How does the effective spring constant of the combined system relate to the spring constants of the individual springs? Postulate what the effective spring constant for the three springs will be.
Check your hypothesis by oscillating a system of three springs and measuring the period.
Explain your observations by considering Hooke's Law and the forces
on each of the component springs.