Lab #1 Simple Harmonic Oscillation 9/7/00

__Objectives__:

In this lab
we will determine between both the mass of the oscillator and the amplitude of
oscillation. We will also verify the
statement _{}. We will begin by
calculating the values of _{} and _{}, next, we will examine the relation between the amplitude
and the period and finally we will examine the relation between the mass and
the period.

__Part 1__:

__Introduction__:

This part of the experiment involves two separate calculations. First we will use the force sensor to directly measure the spring constant of each individual spring. This data will be used to calculate a theoretical period. Next we will use both springs simultaneously. In this section of the experiment, the measure of the force sensor gives a sine wave directly related to that of the acceleration. We use this wave to measure the actual period.

__Data__:

__Spring 1__ __Spring
2__

_{}

_{}

__Data Analysis__:

__Spring 2__:

__Results__:

_{} _{}

_{}

_{}

_{}

__Uncertainty__:

There are two places where uncertainty can become a factor in this section of the experiment. The first is in the measurement of the extension and is approximately ± .001 m. The second involves the precision of the force censor, which is unknown to us at this point in time. Assuming an uncertainty of ±3 % in the force censor, we may estimate a possible uncertainty of slightly over 4 %.

__Part 2__:

__Introduction__:

In this section of the lab, we will repeat the second half of part 1 with varying amplitudes. An examination of the periods calculated will be compared with the varying amplitudes to determine the effect of the amplitude on the period.

__Data__:

m= .26345 kg

__Data Analysis__:

__Results__:

From the graph, we observe that the amplitude has no effect on the period that cannot be explained by experimental uncertainty. The value of the period is 1.875 ± .3%

__Uncertainty__:

There are two sources of uncertainty in this experiment. The first comes from our inability to measure to a precision finer than 1 mm. The second source of error comes from the force sensor used to calculate the period. We do not know the precision of the calibration or the manufacturers accuracy of the sensor.

__Part 3__:

__Introduction__:

In this
part, we will repeat part 2 with a slight modification. This time, instead of varying the amplitude,
we will change the mass of the glider.
We will now be able to determine the relationship between the mass of
the glider and the period of oscillation.
We predict that the period will increase with the mass. We predict that the period and the mass will
be related by the formula _{}, which leads to the formula _{} because _{}

__Data__:

__Data Analysis__:

__Results__:

An
examination of the graph of the mass vs. the period shows that the period
increases with the mass and follows a curve of the type _{}. This corresponds
with our theoretical formula since _{} is a constant and can
equal _{}. Our calculated value
for _{} is 3.6 while the
measured value is 3.68. This gives a
percent difference of 2%.

__Conclusion__:

From Part 1 we determined that the
effective spring constant was 3.051.
This value is well within the value allowed for by the experimental
uncertainty. We can therefore state that
the effective spring constant is equal to the sum of all the individual spring
constants or _{}.

From Part 2, we have confirmed that the amplitude of the oscillation does not vary the period.

In Part 3, we verified that the
relation between the mass and the period is of the type _{}.

In all three sections, our predictions proved correct within the limits of the experimental uncertainty.