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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.

User Rarw
by
9.2k points

1 Answer

5 votes

Answer:

Mass of 17.854 kg is only attached to the spring

Step-by-step 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{(m)/(k)}, here m is mass and k is spring constant

From the relation we can see that


(T_1)/(T_2)=\sqrt{(m)/(m+22)}


(22)/(33)=\sqrt{(m)/(m+22)}

Squaring both side


0.444={(m)/(m+22)}


0.444m+9.777=m

m = 17.584 kg

So mass of 17.854 kg is only attached to the spring

User Kwelsan
by
9.4k points
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