Question

A group of students performed the "Spring–Mass" experiment usinga spring of non-negligible mass Ms kg and spring constant k N/m.The students determined the period of oscillation for sevendifferent values of the hanging mass m. They obtained the followingresults:
m (g) T (s)
50 0.147
70 0.167
90 0.185
110 0.201
130 0.216
150 0.230
170 0.244

Note: In lab the spring's mass was negligible but here you need toinclude 1/3 of Ms with the hanging mass. Consider how this willchange the equation for the spring–mass system.
(a) Use Excel to construct a spreadsheet and do the following. (Youwill not submit this spreadsheet. However, the results will beneeded later in this problem.)
(i) Enter the above data.
(ii) Create a graph of T2 vs. m.
(iii) Use the LINEST function to determine the slope, y interceptand the associated uncertainties.

(b) Record your values below.
slope = ±
y-intercept = ±

(c) What is the formula for the uncertainty in k in terms of theuncertainty in the slope? (Use the following variable as necessary:k and σ_s for the uncertaintyin the slope.)
σ_k =

(d) What is the formula for the uncertainty in Ms the mass of thespring, in terms of the uncertainty in the y intercept andσ_y? (Use the following asnecessary: Ms, yi for the y intercept,σ_s, and slope.)
σ_Ms =

(e) From your value of the slope determine the spring constant k ofthe spring.
k = ±

(f) From your value of the intercept determine the mass Ms of thespring.
Ms = ±