Is it S.H.M?

Let $L$ be the length of the rod and $\ell$ the length of the thread.

Let $x$ the the horizontal distance over which the load $m$ swings outward, and $v$ its horizontal speed. Let $y$ be the vertical distance over which it is displaced. Geometric constraint of the string requires $(\tfrac12x)^2 + (\ell - \tfrac12y)^2 = \ell^2;$ In small angle approximation we ignore the term of order $y^2$ and obtain. $y \approx \frac{x^2}{4\ell}.$ For the energy of the system we may therefore write $E = K + U = \tfrac12mv^2 + mgy = \tfrac12m\left(v^2 + gx^2/2\ell\right) = \text{const.}.$ This describes harmonic motion with angular period $\omega = \sqrt{g/2\ell},$ and period $T = 2\pi/\omega = 2\pi\frac{\sqrt{2\ell}}{\sqrt g}.$ Thus, $k = \boxed{2}$ .

why level 5 ? still by the constraints of the force by string( i don't think i need to tell even that !) , the time period exactly comes which is given in the ques , with k as 2 !:)

consider the above system as a simple pendulum with l= root of l^2+(l/2)^2 and g effective as gcos(theta) and cos(theta) =l/ root of l^2+(l/2)^2