Question

No matter what values of m and k you used for the spring, what is the ratio of the period to k m.

Answer 1

The relationship between the period of an oscillating spring and the attached mass determines the ratio of the period to $\sqrt{\dfrac{m}{k} }$.

Response:

• The ratio of the period to  $\sqrt{\dfrac{m}{k} }$ is always approximately 2·π : 1

How is the value of the ratio of the period to $\sqrt{\dfrac{m}{k} }$ calculated?

Given:

The relationship between the period, T, the spring constant k, and the

mass attached to the spring m is presented as follows;

$T = \mathbf{2 \cdot \pi \cdot \sqrt{\dfrac{m}{k} }}$

Therefore, the fraction of of the period to $\sqrt{\dfrac{m}{k} }$, is given as follows;

$\mathbf{\dfrac{T}{ \sqrt{\dfrac{m}{k} }}} = 2 \cdot \pi$

2·π ≈ 6.23

Therefore;

$T :{ \sqrt{\dfrac{m}{k} }} = 2 \cdot \pi : 1$

Which gives;

• The ratio of the period to  $\sqrt{\dfrac{m}{k} }$ is always approximately 2·π : 1

Learn more about the oscillations in spring here:

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