Question

Show that equations (3) describe the motion of balls of masses $m_1, m_2$, connected with a weightless spring of rigidity $k$ ( $l$ is the length of a unloaded spring, $\left.r_1(t) \leq r_2(t)\right)$. Check an invariance of equations at the passage from one inertial system to another.

   Show that equations (3) describe the motion of balls of masses $m_1, m_2$, connected with a weightless spring of rigidity $k$ ( $l$ is the length of a unloaded spring, $\left.r_1(t) \leq r_2(t)\right)$. Check an invariance of equations at the passage from one inertial system to another.
 
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Principles of Mathematical Modelling: Ideas, Methods, Examples
Principles of Mathematical Modelling: Ideas, Methods, Examples
Alexander A.… 1st Edition
Chapter 3, Problem 1 ↓

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Since they're not explicitly given in the problem, I'll assume they are the following equations of motion for two masses connected by a spring: $$m_1 \ddot{r}_1 = k(r_2 - r_1 - l)$$ $$m_2 \ddot{r}_2 = -k(r_2 - r_1 - l)$$ where $r_1(t)$ and $r_2(t)$ are the  Show more…

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Show that equations (3) describe the motion of balls of masses $m_1, m_2$, connected with a weightless spring of rigidity $k$ ( $l$ is the length of a unloaded spring, $\left.r_1(t) \leq r_2(t)\right)$. Check an invariance of equations at the passage from one inertial system to another.
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