Question

If time period of oscillation of a body connected with a spring is T. Now spring is cut into two equal parts and both parts connected in parallel then period of oscillation of same body is​

Answer 1

So time period of oscillation will become $\frac{T}{2}$  

Explanation:

Let the mass of the body is m, and spring constant is k

So time period is given by $T_1=2\pi \sqrt{\frac{m}{k}}$----eqn 1

Now spring is cut into two equal parts so spring constant will become 2k

Now the parts are connected in parallel so equivalent spring constant will become $k_{eq}=2k+2k=4k$

Now new time period is given  by $T_2=2\pi \sqrt{\frac{m}{4k}}$---eqn 2

Dividing eqn 1 by eqn 2

$\frac{T_1}{T_2}=\sqrt{\frac{m}{k}\times\frac{4k}{m} }$

$T_2=\frac{T_1}{2}$

So time period of oscillation will become $\frac{T}{2}$  

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If the time period of oscillation of mass m suspended from a spring is 2s,the time period of mass 4m will be

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Answer 2

Answer:spring cut into equal parts so l1=l2 find k1 and k2 =2k so net k=4k soT'=2π√m/4k. T'=T/2

Explanation: