Assume two springs with constant $c_1$ and $c_2$ are based in the following scenarios. Figure out the masses for equal displacement

Question

Assume two springs with constant $c_1$ and $c_2$ are based in the following scenarios. Figure out the masses for equal displacement.

More specifically I am to figure out what masses $m_1$, $m_2$ will produce equal displacements $x_1$ and $x_2$

Scenario 1: When the two springs are hung from separate supports

Scenario 2: With one spring below the other.

I have never taken physics before and I'm really unsure how to tackle this problem. If anyone can help that will be great.

Answer 1

I'm not sure I understood the details of the system. If I understood correctly, here is my solution for one of the scenarios you described.

Answer 2

Hung separately;

$$M_1g = C_1X_1$$

$$M_2g = C_2X_2$$

Since the displacements are equal therefore we have;

$$M_1g = C_1X_1$$

$$M_2g = C_2X_1$$

Therefore;

$$\frac{M_1g}{C_1} = \frac{M_2g}{C_2}$$

Therefore;

$${M_1} = \frac{M_2C_1}{C_2}$$