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| Consider a compound Atwood machine composed three masses (labeled \(m_1 , m_2, \text{and} m_3\) ) attached by two massless ropes through two massless pulleys in a constant gravitational field with acceleration \(g\).Solve the equations of motion and show that the accelerations are given by \begin{eqnarray} \ddot{x}&=&g\left(\frac{m_1m_+-(m_+-m_-)^2}{m_1m_++(m_+-m_-)^2}\right)\\ \ddot{y}&=&g\left(\frac{2m_1m_-}{m_1m_++(m_+-m_-)^2}\right) \end{eqnarray} |  |
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