Question

A spring has a period of 1 s when a 0.200 kg mass hung from the end of it. If the mass at the end is changed to 0.100 kg, will the period change?

Answer 1

When the mass of the spring changed from 0.2kg to 0.1kg, the time period changed from 1 sec to 0.5 seconds

Explanation:

Given-

Mass, m1 = 0.2kg

Time period, T1 = 1s

m2 = 0.1 kg

T2 = ?

We know,

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

where,

T = Time period

m = mass

k = spring constant

From the equation, we can see that T is directly proportion to the square root of mass, m

T ∝ √m

So,

If m1 = 0.2kg , T1 = 1s and m2 = 0.1kg

The T2 would be:

$\frac{T1}{T2} = \frac{m1}{m2} \\\\\frac{1}{T2} = \frac{0.2}{0.1}$

$T2 = \frac{1}{2} \\\\T2 = 0.5sec$

Therefore, when the mass of the spring changed from 0.2kg to 0.1kg, the time period changed from 1 sec to 0.5 seconds