LAB #10: Simple Harmonic Motion
Theory:
• What is simple harmonic motion (SHM)? Explain and draw an example.
• Define Hooke’s Law.
• Equations for position, velocity and acceleration vs. time for SHM.
• What is amplitude? Position, velocity and acceleration amplitudes.
Experiment:
1. Determine the spring constant k
a. Hanging different masses (from 50 to 80gr) measure the spring
displacement ∆X
•
•
•
mass of a spring Msp=
mass of a hanger mh=
equilibrium position (distance from the floor to the bottom on the
spring when nothing is hanging) Xeq=
•
∆X = X eq − X
b. The spring constant is the slope of the F vs. x line
2. Observe the motion of oscillating mass mo, using the Motion Sensor (mo=70gr
including hanger). Pull the mass downward and let it go. The spring with mass
will start to oscillate. As a result you’ll get 3 graphs; position, velocity and
acceleration vs. time.
a. Fit them using SINE FIT. Coefficients B from the sine series fits are period
of oscillations and should have the same values form all three graphs.
Calculate frequency f=1/B and its uncertainty using B from position plot.
b. Calculate ωmeas=2πf and δωmeas
k
(where m=mo+1/3Msp) and δωth
m
Compare ωmeas with ωth
Determine measured amplitudes that are A coefficients from the sine fits.
Determine calculated amplitudes V0=X0ωth and V0=X0ωth2 and their
uncertainties.
Compare measured with calculated amplitudes.
c. Calculate ω th =
d.
e.
f.
g.