Question

A block of mass $m$ is connected to three springs, each of spring constant $k$ as shown in figure. The block is pulled by $x$ in the direction of $C$. Find resultant spring constant=?

• A. $k$
• B. $2k$
• C. $3k$
• D. $\frac{3k}{2}$

Answer 1

The correct option is D $\frac{3k}{2}$

Equating forces along X-axis, we get:
$F_{net}=-(kx+ky\cos 60+ky\cos 60)$ where $x$ and $y$ are displacements of the other two springs.
Now, $\Delta y=\Delta xcos{60}^o$ from diagram.
$\therefore F_{net}=-\frac{3}{2}kx$
$\therefore k_{eq}=\frac{3}{2}k$