Question

If the total hanging massif 50g increased 4 times without changing the spring constant, how would this affect period of oscillation and/or the frequency?

Answer 1

The formula for the period of oscillation:

$$T=2\pi\sqrt{\frac{m}{k}}$$

Thus, for the period:

$$\frac{T'}{T}=\frac{2\pi\sqrt{\frac{4m}{k}}}{2\pi\sqrt{\frac{m}{k}}}=2$$

Therefore,

$$\frac{f'}{f}=\frac{T}{T'}=\frac{1}{2}$$