Question

14. Time period of the block in the shown system is
​

Answer 1

Explanation:

the time period of the block

= 2pi under root 3m/2k

the first two springs are connected in parallel and third spring is connected in series

Answer 2

Time period of the block in the shown system is  $T=2\pi\sqrt{\dfrac{3m}{2k}}}$ .

We need to find the the time period of the given system .

The time period of the block in the spring is :

$T=2\pi\sqrt{\dfrac{m}{k_{eq}}}$   ..... 1

Here , $k_{eq}$ is the equivalent spring constant :

We know , equivalent spring constant parallel is given as :

$k_{eq}=k_1+k_2$

And in series is given as :

$\dfrac{1}{k_{eq}}=\dfrac{1}{k_1}+\dfrac{1}{k_2}$

Here , the equivalent spring constant for parallel is given as :

$k_{eq1}=k+k\\k_{eq1}=2k$

Therefore , it is in series with the other k spring :

$\dfrac{1}{k_{eq}}=\dfrac{1}{k}+\dfrac{1}{k_{eq1}}\\\\k_{eq}=\dfrac{2}{3}k$

Putting this in equation 1 , we get :

$T=2\pi\sqrt{\dfrac{3m}{2k}}}$

Hence , this is the required solution .

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