$\begin{array}{1 1}14.9N/m\\15.9N/m\\24.9N/m\\17.9N/m\end{array} $

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Answer : 14.9N/m

We place the origin of our coordinate system at the top of the spring,with the positive direction upward,as is customary.

Then $x_0=-15.4cm$ and $x=-28.6cm$.

According to Hooke's law,the spring force is $F_s=-k(x-x_0)$

Also,we know the force exerted on the spring was provided by the weight of the 0.200-kg mass :

$ F=-mg $

$ \;\;\;=-(0.200 kg)(9.81m/s^2) = -1.962 N $

Again,the negative sign indicates the direction.

Now we can solve the force equation for the spring constant :

$ k =-\large\frac{F_s}{x-x_0}=-\large\frac{1.962N}{(-0.286m)-(-0.154m)} $

$\;\;\;=14.9N/m$

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