PHYSICS 123 EXPERIMENT NO. 7
SIMPLE HARMONIC MOTION
The phenomenon of simple harmonic motion is studied for masses on springs and
suspended pendulums. The physical basis of these oscillations is that the force exerted on
a mass is proportional to the negative of the displacement of the mass from equilibrium.
Equipment
One air track with glider, string, small masses, photogates, one simple pendulum, one
meter stick pendulum, one computer and interface box.
photo gate
spring attached to glider
and end of track (barely
visible on this photo)
Flag on glider
Glider
spring attached to glider
and end of track
pulley, from which a
string with weight is
suspended
interface box
10 and
20 gram
masses
50 gram
weight
hanger
Method:
Throughout this experiment, a system (glider between springs, assorted pendulums) will
be displaced from equilibrium and the period T, of oscillation will be measured. For the
various oscillators, the dependence of the period on amplitude will be assessed. For true,
simple harmonic motion, there should be no dependence.
Procedure:
I. MEASUREMENT OF SPRING CONSTANT:
The phenomenon of simple harmonic motion is studied for masses on springs. The
physical basis of these oscillations is that the force exerted on the mass by the spring
is proportional to the negative of the displacement of the mass from equilibrium.
Pulley
Spring
Air Track
Glider
mass of weight hanger + 20 gram
weight = equilibrium
Record the equilibrium position of the glider on an air track. Attach a piece of string
to the glider and lay it on the pulley with a mass m suspended from the free end of
the string. Measure the (displacement of the glider. Be sure that the string moves
freely and does not scrape. Repeat with three other masses for a total of four
measurements. Make sure you are taking the difference between your position
readings and the equilibrium position as your data. Graph the weight of the
masses, mg, versus x, the displacement of the glider from equilibrium. Q1: Is
there a linear relationship between the weight and the displacement? Measure
the slope of the line fitted to these points on your graph. As you have determined,
the slope is k, the spring constant, from F = -kx (Hooke's Law).
II
PERIOD OF GLIDER, SPRING SYSTEM: Attach the glider to the two springs and
place the glider on the air track so that the ‘metal flag’ atop the glider is near to, but
does not obstruct the photo gate when the glider is at equilibrium.
Metal Flag
Glider
Photo Gate
On the computer, go to “MISCELLANEOUS TIMING MODES” on the Main Menu
screen, then chose “PENDULUM TIMER”, then “Normal Time Display”. This
mode allows the computer to measure the period T. Make sure the “SET” button is
pushed on the gray interface box. Set the glider in motion by displacing it from the
equilibrium position slightly and make sure that for all oscillations, the flag on top of
the glider completely passes through the photo gate. Push the “STOP” button on the
gray interface box when you see ~10 rows of data on the computer screen. To get
the period take the average of the 5 measurements.
a. Measure the period of oscillation of the glider.
b. Repeat the measurement of the period of oscillation after attaching one and then two
heavy masses to the glider. Q2: Is the measured T = 2 m/k for each combined
mass in agreement with what theory predicts?
c. Remove the masses and measure the period for 5 different amplitudes. Q3: Does
the period change? How does this relate to the theoretical prediction?
PHY-123 Laboratory No. 7
III. THE RETURN OF THE SIMPLE PENDULUM. Place a mass m at the end of the
length L of a pendulum. Record the period of oscillation for at least six different
amplitudes. Make at least some of the pendulum swings rather large, as long as the
pendulum does not begin acting like a demolisher's wrecking ball on your lab partner!
Q4: Does T = 2 L/g for all amplitudes? Does T have any m dependence?
(Hint: re-read the section on the pendulum in your physics text book)
IV. THE PHYSICAL PENDULUM. Attach two paper clips to the end of a meter stick to
make a pendulum. Hang the meter stick by the paper clips between your figures and
repeat the steps for the simple pendulum to calculate the period of oscillation for at least
six different amplitudes. Q5: In this case T = 2 (I/mgL) where I is the moment of
inertia, m the mass, and L the distance from the pivot point to the center. Knowing
the moment of inertia (which you can look up in your textbook) do your values of T
agree with what you should get? (Hint: To calculate T you do not need to weigh the
meter stick)
What you need:
1. 4 measurements of x for the spring system
2. Graph of mg vs. x
3. Calculation of slope
4. Measurement of the period of oscillation of glider
5. Measurement of the period of oscillation of glider and additional masses
6. Measurement of the period of oscillation of glider for 5 different amplitudes
7. Simple pendulum calculations
8. Physical pendulum calculations
9. Answers to all questions