The time period of a spring-mass system is T . If this spring is cut into two parts, whose lengths are in the ratio 1 : 2 , and the same mass is attached to the longer part, the new time period will b

Question

The time period of a spring-mass system is T . If this spring is cut into two parts, whose lengths are in the ratio 1 : 2 , and the same mass is attached to the longer part, the new time period will be

TestHub · Accepted Answer

The spring-mass system oscillates in SHM. Its time period is given by

$T = 2 π \sqrt{\frac{m}{k}}$

When spring is cut in ratio $1 : 2$ , the new spring constant is $k' = 3 k /2$ (for the longer part)

$∴$ $\frac{T}{T'} = \sqrt{\frac{\frac{3 k}{2}}{k}}$

$\Rightarrow$ $T' = \sqrt{\frac{2}{3}} T$

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