Two springs of stiffness k connected as shown in the figure are not deformed. What mass should the load be suspended from the point where the springs are connected so that it falls a small distance x to the equilibrium position?

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    <h3 id="back-link"><a href="/#3.1">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $3.1.11.$ Two springs of stiffness $k$ connected as shown in the figure are not deformed. What mass should the load be suspended from the point where the springs are connected so that it falls a small distance $x$ to the equilibrium position?

    <h3>Solution</h3>
    <p>
        Each spring will have an elastic force when stretched

$$F_y=k\Delta l=kx\cos\alpha$$
Condition of equality of forces
$$mg=2F_y\cos\alpha =2kx\cos^2 \alpha$$
Where, weight of cargo
$$\boxed{m=\frac{2kx\cos^2 \alpha}{g}}$$

    <h4>Answer</h4>
    <p>
        $$m=\frac{2kx\cos^2 \alpha}{g}$$
    </p>

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