Physics 11 IB Oscillating Mass Design Lab (D/DCP/CE)
Research Question
The aim of this experiment is to identify and investigate the various factors that affect the period of
oscillation of a mass hanging on a spring.
Hypothesis
We have:
ω = (k/m)1/2
And therefore:
And:
Where:
ω = (2π/T)
ω = (2π/T) = (k/m)1/2
T = 2 π (m/k)1/2
The above formula indicates that the only factors which could affect the period T of an oscillating mass
are the mass, m, of the oscillating object, and the spring constant, k.
If k is kept constant, and m is increased, T increases too, and the oscillation is slowed down. Conversely,
if m decreases, T is decreased too, and the oscillations occur more frequently (provided k is kept
constant).
On the other hand, if the mass, m, is kept constant and k is increased (by switching springs) then T
decreases and the oscillations become faster. Conversely, if k is decreased, then T will increase and the
oscillations will occur less frequently (provided the mass of the object remains constant).
Variables:
Independent:
Mass, m, of hanging object, the spring constant k
Dependent:
The period, T, of the pendulum
Controlled:
The mass, m, of the object (if k is the independent variable) and the spring constant k (if
m is the independent variable).
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Materials:
Elastic spring or elastic bands
Set of masses
Meter stick
Stop watch
Vernier Labpro Equipment. (You must set this up yourself)
Part 1: Determining the Spring Constant of Your Spring
1. Measure the mass of your spring.
2. Measure the length of your spring as accurately as you can.
3. Attach your spring to the ceiling and then let the spring hang down. Add a small mass of 100
– 200g to your spring. Measure this new length accurately.
4. The value of k is obtained from mg/x; (where x is the change in length of the spring) will give
you the spring constant of the spring.
Part 2: Collecting Period Data for an Oscillating Mass.
1. Attach a 0.100 kg mass to the end of your hanging spring. Gently pull down your spring a
few centimeters and release.
2. Note how the spring and mass oscillates up and down.
3. Come up with a method of collecting data points for determining the relationship between
the mass applied to the spring and the period of its oscillations.
4. Prepare a data table showing your collected data.
Analysis:
1. Plot a graph of Period vs mass.
2. Note the shape of this graph. Attempt to straighten this graph by plotting period against
some function of the mass.
3. Plot this new graph to show the linear relationship and determine the slope of the straight
line.
4. Use this slope to calculate the spring constant of your spring and compare it the original
value calculated in Part 1.
5. What happens to the period if the mass or spring constant is doubled? By what factor must
one scale m or k in order to quadruple the period?
Conclusion:
Discuss how accurate this experiment was to the original equation. Take into account error
sources.
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