spring- finding k and mass?
An object of mass 2.20 kg is oscillating freely on a vertical spring with a period of 0.690 s. Another object of unknown mass on the same spring oscillates with a period of 1.20 s.
Find the spring constant k.
(b) Find the unknown mass.
Thank you in advance
- Anonymous1 decade agoFavorite Answer
The period (T1) of a mass (m1) on a spring(k) is:
T1 = 2 pi sqrt (m1/k)
Solve for the spring constant:
k = 4 pi^2 m1 / T1^2
Likewise, the period (T2) of a mass (m2) on the same spring(k) is:
T2 = 2 pi sqrt (m2/k)
Solve for the mass:
m2 = k T2^2 / (4 pi^2)
And plug in the spring constant you already solved for:
m2 = (4 pi^2 m1 / T1^2) T2^2 / (4 pi^2)
= m1 (T2/T1)^2
Or you could have gotten that last result directly just by noting that the mass is proportional to the square of the period (instead of plugging in k and canceling).
Anyway, they give you the first mass(m1) and both periods (T1 and T2), Now plugnchug for the spring constant(k) and second mass(m2).