First slide

Simple hormonic motion

Question

A spring of spring constant K is cut into n equal parts, out of which r parts are placed in parallel and connected with mass m as shown in figure. The time period of oscillatory motion of mass m is

Moderate

A

T = $2 π \sqrt{\frac{m}{nrK}}$
B

$T = 2 π \sqrt{\frac{nrm}{K}}$
C

$T = 2 π \sqrt{\frac{rm}{nK}}$
D

$T = 2 π \sqrt{\frac{nm}{rK}}$

Solution

$K . l = k^{'} \times \frac{l}{n} = constant$
new spring constant for each part is $K^{'} = nK$
Now r part are taken in parallel
so $K_{eq} = nrk$
Time period = $2 π \sqrt{\frac{m}{K_{eq}}} = 2 π \sqrt{\frac{m}{nrK}}$

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