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{(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{(2.0)/(200) } \\ \\ T= 2\sqrt{(1)/(100) }\\ \\ T= 2*(1)/(10)\\ \\ T= (1)/(5)=0.2`

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