The position graph should show a sinusoidal if it has

6. The position graph should show a sinusoidal, if it has flat regions or spikes,
reposition the Motion Detector and try again;
7. Fit a sinusoidal curve and record on Table II your values of A, B, and C;
9. Using your values of A, B, and C determine the frequency and period of oscillation.
Record the period T and frequency f of this motion in your data table;
10. On Table III (for PHY2048L only) write the equations of y(t) and v(t);
11. Repeat Steps 1 – 10 with different five other masses.
DATA:
Length of the Spring: L
0
= 0.13 m Real Constant: 20.0 N/m
Table I: Hooke’s Law
Trials 1 2 3 4 5 6
Mass
m(kg)
0.200 kg 0.400 kg 0.600 kg 0.800 kg 1.00 kg 1.20 kg
Force on the Spring
F
s
(N)
1.96 N 3.92 N 5.88 N 7.84 N 9.80 N 11.8 N
Length
L(m)
0.180 m 0.280 m 0.380 m 0.480 m 0.570 m 0.665 m
Increase in Length
ΔL (m)
0.0500 m 0.150 m 0.250 m 0.350 m 0.440 m 0.535 m
Table II: Oscillation

Trials 1 2 3 4 5 6
Mass
m(kg)
0.200 kg 0.400 kg 0.600 kg 0.800 kg 1.00 kg 1.20 kg
A(m) 0.0412 m 0.0374 m 0.0491 m 0.0411 m 0.0541 m 0.0487 m
B(rad/s) 9.76 rad/s 7.00 rad/s 5.74 rad/s 5.33 rad/s 4.47 rad/s 4.11 rad/s
C(rad) 3.99 rad 3.73 rad 3.53 rad 4.59 rad 4.83 rad 5.94 rad
T(s) 0.628 s 0.889 s 1.09 s 1.26 s 1.40 s 1.54 s
T
2
(s) 0.394 s
2
0.790 s
2
1.19 s
2
1.59 s
2
1.96 s
2
2.37 s
2
f (Hz)
1.59 Hz 1.13 Hz 0.919 Hz 0.800 Hz 0.712 Hz 0.650 Hz
EVALUATION OF DATA:
Graph 1: Force on the Spring vs. Displacement
Equation:
F
s
(
N
)
= k
(
N
m
)
∆ L
(
m
)
+ b ( N )
Relationship: The force on the spring is directly proportional to the displacement (linear
relationship).
Slope: The slope of the line represents the spring constant (k) which is in Newton’s per
meter.
Y-Intercept: The y-intercept is close to 1 N. There may be some errors when measuring the
lengths of the spring for each trial.

Graph 2 (Power): Period vs. Mass
Equation:
y = ax
k

T = A L
B
Relationship: The graph is a power function and in order to make it linear, I have to square
the period. As seen on the graph, the function is a side opening parabola where the y axis
squared (T 2 ) is proportional to the x axis (M). Therefore, to make this function linear (to
make it fit into the equation of the line y=mx+b), the period must be squared to have a
proportional relationship. (Note: Proportional means linear.) Once I have the linear graph, I
will know the relationship, the equation, and the slope of the line.
Graph 2 (Linear): Period Squared vs. Mass