Question

A mass attached to a spring oscillates with a period of 22 sec. After 22 kg are​ added, the period becomes 33 sec. Assuming that we can neglect any damping or external​ forces, determine how much mass was originally attached to the spring.

Answer 1

Answer:

Mass of 17.854 kg is only attached to the spring    

Explanation:

We have given time period in first case is 22 sec

Let initially mass is m

After 22 kg are added the period becomes 33 sec

Time period of spring mass system is

$T=2\pi \sqrt{\frac{m}{k}}$, here m is mass and k is spring constant

From the relation we can see that

$\frac{T_1}{T_2}=\sqrt{\frac{m}{m+22}}$

$\frac{22}{33}=\sqrt{\frac{m}{m+22}}$

Squaring both side

$0.444={\frac{m}{m+22}}$

$0.444m+9.777=m$

m = 17.584 kg

So mass of 17.854 kg is only attached to the spring