A spring with a mass of 400.0 g is set into simple harmonic motion. The graph of the force of the spring vs. displacement is shown. The data of the position of the spring vs. time while it is oscillating are also shown.

t (s) y (m)
0.0 0.00
0.2 0.09
0.4 –0.07
0.6 –0.04
0.8 0.10
1.0 –0.03
1.2 –0.08
1.4 0.09
1.6 0.01
1.8 –0.10
2.0 0.06
2.2 0.05
2.4 –0.10
2.6 0.02
2.8 0.09
3.0 –0.08
3.2 –0.03
3.4 0.10
3.8 –0.07
4.0 0.09

Do the following:
a. Determine the spring constant from the graph.
b. Make a position vs. time graph for the spring’s motion.
c. Determine the amplitude and period of the spring’s motion from your graph.
d. Calculate the period of the spring’s motion using the spring’s period equation.
e. Determine the percent error by comparing the period from the graph (experimental value) to the calculated value (accepted value).
Answer:

OK, so I'm not the best at this but i think I can help a lil bit,
A. by constant does it mean the way it moves? If so, a constant would be 00.75 if you can scale it out in your mind.
B. I think you are supposed to make a graph with letter A's info
C. hmmm, (confusing) I think you need to figure out what we did in A. 00.75 but I'm not really sure...
D. SO here we need to look at the springs motion, which the displacement would be about 00.020, But i dont really get what the top is... :/ SO, I'm not that much of a help... on alot of these :(
E.what is E? it says : Answer:??? 00.025 I'm SO sorry this is much more complicated than i realized :/ I did the best i could :(

briannawenger briannawenger · Answer 2 · 2021-01-24T08:42:14-05:00

Answer:

Determine the spring constant from the graph.

Make a position vs. time graph for the spring’s motion.

Determine the amplitude and period of the spring’s motion from your graph.

Calculate the period of the spring’s motion using the spring’s period equation.

Determine the percent error by comparing the period from the graph (experimental value) to the calculated value (accepted value).

Answer:

a- k = (y_2 - y_1) / (x_2 - x_1)=(4.75-1.78)/(0.083-0.006)=40 N/m

b- graph

C- The maximum amplitude of displacement y = 0.1 m The time period of the displacement T_a = 2 s / 3 cycles = 0.67s

D- T_theo = 2*pi*sqrt(m/k) T_theo = 2*pi*sqrt(0.4/40) = 0.628 s

E- RE = ( T_a - T_theo) / T_theo * 100 RE = (0.67 - 0.62831) / 0.62831 * 100 = 6.63% - The value obtained is within the 10% tolerance of experimental Error. Hence, we can conclude that the experiment was conducted reasonably.

Explanation: