Q.

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

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a

T = 2πmnrK

b

T = 2πnrmK

c

T = 2πrmnK

d

T =2πnmrK

answer is A.

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Detailed Solution

K.l = k'×ln = constantnew spring constant for each part is K' = nKNow r part are taken in parallelso Keq = nrkTime period = 2πmKeq = 2πmnrK
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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