7. At the ends of a vertically positioned homogeneous spring, two small loads are fixed. Above is a load with mass $m_{1}$, and below is $-m_{2}$. A person grabbed the middle of the spring and held it vertically in the air. In this case, the upper half of the spring was deformed by $x_{1}=8 \mathrm{~cm}$, and the lower half by $x_{2}=15 \mathrm{~cm}$. After that, he placed the spring on a horizontal surface without flipping it and released it. Determine the magnitude of the spring's deformation in this case. Neglect the size of the person's hand compared to the length of the spring.

## $(15$ points)
Answer: 16 cm

Solution. If the stiffness of the spring is $k$, then the stiffness of half the spring is $2 k$ (4 points). For the situation where the spring is held by a person: $m_{1} g=2 k x_{1}$ (4 points).

For the situation where the spring stands on a surface: $m_{1} g=k x$ (4 points). We obtain that $x=2 x_{1}=16$ cm (3 points).