First slide

Applications of SHM

Question

Time period of a spring mass system is T. If this spring is cut into two parts whose lengths are in the ratio 1:3 and the same mass is attached to the longer part. The new time period will be

Moderate

A

$\sqrt{\frac{3}{2}} T$
B

$\frac{T}{\sqrt{3}}$
C

$\frac{\sqrt{3}}{2} T$
D

$\sqrt{3} T$

Solution

The spring mass system oscillates in SHM, its time period is given by $T=2π \sqrt{\frac{m}{K}}$
When spring is cut into ratio of 1:3 the new time constant is $K^{1} = 3 K$ $∴ \frac{T}{T^{1}} = \sqrt{\frac{3K}{K}}$
$T^{1} = \frac{T}{\sqrt{3}}$

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