# 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

### 1 Answer

- Anonymous1 decade agoBest 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).