Experiment 10

Hooke's Law and Simple Harmonic Motion

Objectives

To see if masses on springs obey Hooke's law and to find the constant in the law.

Introduction

If a mass, m, is hung from a spring it will come to equilibrium at a point where the spring pulls up as hard

as gravity pulls down. If the mass is lowered a distance, x, the spring will increase its pull by supplying an

additional amount of force

where k is the "spring constant" and equation 1 is "Hooke's Law." There will thus be a net upward force

restoring the mass to the equilibrium position. If the mass is raised a distance x above the equilibrium

position, the pull of the spring against gravity will be reduced by kx and the net force will be kx downward.

The net force is therefore always toward the equilibrium position. The resulting motion is vibratory and is

called simple harmonic motion. It has a period

Procedure

Hang a spring from a stand and suspend a weight hanger from the lower end of the spring. Place enough

mass on the holder to pull the coils apart. Record the total mass suspended from the spring and record

the position of the bottom of the hanger.

Add a mass increment sufficient to lower the hanger about 1 cm and record the increment and the new

position of the hanger. Set the system into a vertical vibration of about 5 cm amplitude. Time 20 of the

oscillations and find the period of one oscillation.

Repeat the above step for 9 additional, similar increments. Form a table of these ten masses with their

corresponding periods and positions. Make an additional column for the square of each period.

Graphs

1)     Plot weight in dynes versus position in cm. This is a plot of Hooke's Law and its slope should be

k. Do a least squares fit.

2)     Plot the square of the period versus the total mass. This is a plot of equation 2 squared so its

slope should be 4π²/k. From a least squares fit to this line, find the value of k and compare it

with the k value of the first plot.