Question

10. A weight hangs on a spring. The vibration period of that weight is the time in which it makes a complete cycle in motion. Suppose the relationship between the vibration period "T" (in seconds) and the weight "w" (in kilograms) is given by T = 2 √(w / 200). Find the period T for a spring with a hanging weight of 2.0 kilograms.

Answer 1

The vibration period of the spring will be 0.2 seconds

Explanation

The relationship between the vibration period "T" (in seconds) and the weight "w" (in kilograms) is given by...

$T= 2\sqrt{\frac{w}{200}}$

Given that, the weight(w) = 2.0 kilograms

So, plugging w = 2.0 into the above equation, we will get...

$T= 2\sqrt{\frac{2.0}{200} } \\ \\ T= 2\sqrt{\frac{1}{100} }\\ \\ T= 2*\frac{1}{10}\\ \\ T= \frac{1}{5}=0.2$

So, the vibration period of the spring will be 0.2 seconds.