Question

A simple pendulum of mass m and length l hangs from a trolley of mass M running on smooth horizontal rails. The pendulum swings in a plane parallel to the rails. Using the position x of the trolley and the angle \theta of the pendulum such that \theta =0 corresponds to the pendulum pointing vertically down as generalized co-ordinates, write down the Lagrangian function, and Lagrange's equations. Obtain an equation of motion for \theta alone. [30]

Name: a simple pendulum of mass m and length l hangs from a trolley of mass m running on smooth horizontal rails the pendulum swings in a plane parallel to the rails using the position x of the tr 26985
Uploaded: 2025-05-28T15:45:08-08:00
Duration: 1 min 18 s
Channel: Andreas Papavassiliou
Description: a simple pendulum of mass m and length l hangs from a trolley of mass m running on smooth horizontal rails the pendulum swings in a plane parallel to the rails using the position x of the tr 26985

          A simple pendulum of mass m and length l hangs from a trolley of mass M running on smooth horizontal rails. The pendulum swings in a plane parallel to the rails. Using the position x of the trolley and the angle \theta  of the pendulum such that \theta =0 corresponds to the pendulum pointing vertically down as generalized co-ordinates, write down the Lagrangian function, and Lagrange's equations. Obtain an equation of motion for \theta  alone.
[30]

a simple pendulum of mass m and length l hangs from a trolley of mass m running on smooth horizontal rails the pendulum swings in a plane parallel to the rails using the position x of the tr 26985

Added by Jesus E.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Andreas Papavassiliou

05/28/2025

Step 1

A simple pendulum of mass m and length $l$ hangs from a trolley of mass M running on smooth horizontal rails. The pendulum swings in a plane parallel to the rails. Using the position x of the trolley and the angle $\theta$ of the pendulum such that $\theta = 0$ Show more…

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A simple pendulum of mass m and length l hangs from a trolley of mass M running on smooth horizontal rails. The pendulum swings in a plane parallel to the rails. Using the position x of the trolley and the angle \theta of the pendulum such that \theta =0 corresponds to the pendulum pointing vertically down as generalized co-ordinates, write down the Lagrangian function, and Lagrange's equations. Obtain an equation of motion for \theta alone. [30]