You hang different masses M from the lower end of a vertical spring and measure

Question

You hang different masses M from the lower end of a vertical spring and measure the period T for each value of M. You use excel to plot T^2 (in s^2) on the y-axis versus M (in kg) on the x-axis. The equation for the straight line that gives the best fit to your data is
y= 0.0428x + 0.00100
What is the mass of the spring?
You hang different masses M from the lower end of a vertical spring and measure the period T for each value of M. You use excel to plot T^2 (in s^2) on the y-axis versus M (in kg) on the x-axis. The equation for the straight line that gives the best fit to your data is
y= 0.0428x + 0.00100
What is the mass of the spring?

y= 0.0428x + 0.00100
What is the mass of the spring?

Explanation / Answer

We know that the necessary equation of period ,T is,

T2 = 4*3.142*M/k + 4*3.142*m/k
where M is the hanging mass
and m is the spring mass
and k is the spring constant
and T is the period

For y = T2 = 0.0428x + 0.00100
x is the hanging mass M (your independent variable).

Therefore 0.0428 = 4*3.142 / k, so
k = 921 N/m

(b) 0.00100 = 4*3.142m / 921 N/m, so
m = 0.023 kg = 23 g

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