- #1

Amitayas Banerjee

- 31

- 2

**<<Moderator's note: Moved from a technical forum, no template.>>**

Description of the system:

The masses m

_{1}and m

_{2}lie on a smooth surface. The masses are attached with a spring of non stretched length l

_{0}and spring constant k. A constant force F is being applied to m

_{2}.

My coordinates:

Left of m

_{1}there is a stationary wall. The distance between m

_{1}'s left surface and the wall is represented as y and the distance between the right and left surfaces of m

_{1}and m

_{2}, respectively, is represented as x.

What my brain says:

The kinetic energy of this system is equal to the sum of kinetic energies of the two masses, i.e,

$$\frac{1}{2}m_1 \dot{y}^2 + \frac{1}{2}m_2 (\dot{x}+\dot{y})^2$$

and the potential energy is just the spring potential, i.e,

$$\frac{1}{2} k (x-l_0)^2$$

Therefore, the Lagrangian seems to be,

$$L=\frac{1}{2}m_1 \dot{y}^2 + \frac{1}{2}m_2 (\dot{x}+\dot{y})^2 - \frac{1}{2} k (x-l_0)^2$$

Now, the generalized force is

$$F\cdot \frac{\partial {(x+y)}}{\partial x}$$

So, the equations of motion seem to be,

$$\frac{d}{dt}(\frac{\partial L}{\partial {\dot x}}) - \frac{\partial L}{\partial { x}}=F$$

and

$$\frac{d}{dt}(\frac{\partial L}{\partial {\dot y}}) - \frac{\partial L}{\partial { y}}=0$$

Is this correct? Or am I missing something? Please help me figure out the mistakes.

#### Attachments

Last edited by a moderator: