Question

The bob of a simple plane pendulum of mass $m_0$ and length $l_0$ is connected to two small blocks, one of mass $m_1$ by a dashpot, and the other of mass $m_2$ by a spring. The dashpot (with dashpot constant $c$) and spring (with spring constant $k$) are both ideal and massless. The spring is unstreched when the pendulum is vertical and the masses are at the positions shown. An external force $F(t)$ acts on $m_2$. Assume small motions such that the dashpot and the spring remain almost horizontal at all times. Note that gravity acts. i. How many degrees of freedom does the system have? Pick generalized coordinates and describe the generalized coordinates clearly. ii. Find the equation(s) of motion using Lagrangian approach.

          The bob of a simple plane pendulum of mass $m_0$ and length $l_0$ is connected to two small blocks, one of mass $m_1$ by a dashpot, and the other of mass $m_2$ by a spring. The dashpot (with dashpot constant $c$) and spring (with spring constant $k$) are both ideal and massless. The spring is unstreched when the pendulum is vertical and the masses are at the positions shown. An external force $F(t)$ acts on $m_2$. Assume small motions such that the dashpot and the spring remain almost horizontal at all times. Note that gravity acts.
i. How many degrees of freedom does the system have? Pick generalized coordinates and describe the generalized coordinates clearly.
ii. Find the equation(s) of motion using Lagrangian approach.

The bob of a simple plane pendulum of mass m0 and length l0 is connected to two small blocks, one of mass m1 by a dashpot, and the other of mass m2 by a spring. The dashpot (with dashpot constant c) and spring (with spring constant k) are both ideal and massless. The spring is unstreched when the pendulum is vertical and the masses are at the positions shown. An external force F(t) acts on m2. Assume small motions such that the dashpot and the spring remain almost horizontal at all times. Note that gravity acts.
i. How many degrees of freedom does the system have? Pick generalized coordinates and describe the generalized coordinates clearly.
ii. Find the equation(s) of motion using Lagrangian approach.

Added by Juan M.

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