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## Homework Statement

Take the x-axis to be pointing perpendicularly upwards.

Mass ##m_1## slides freely along the x-axis. Mass ##m_2## slides freely along the y-axis. The masses are connected by a spring, with spring constant ##k## and relaxed length ##l_0##. The whole system rotates with constant angular velocity ##\omega## around the x-axis. Determine the Lagrangian in terms of generalized coordinates ##x## and ##y##.

## Homework Equations

$$L = T - U$$

$$F=mg$$

$$F=-kx$$

$$P.E. = mgh$$

$$P.E. = -\frac{1}{2}kx_e^2$$

## The Attempt at a Solution

So ##m_1## is affected by gravity so we have ## -m_1gx ##. The potential in the string is ##\frac{1}{2}k(d-l_0)^2## where ##d^2 = x^2 + y^2##.

So $$U = -m_1gx + \frac{1}{2}k(d-l_0)^2$$

$$T = \frac{1}{2}m_1\dot{x}^2 + \frac{1}{2}m_2\dot{y}^2$$

Is this correct? It feels wrong, but I don't know why. I think my ##T## is wrong though. Shouldn't it be zero? But if it is, I cannot get any eom, later on. I am confused by the fact that I am working within a non-inertial frame, the rotating one.