The dynamic system shown below consists of a cart of mass M carrying a simple pendulum L.
Question:
The dynamic system shown below consists of a cart of mass M carrying a simple pendulum L. The cart moves vertically. It is constrained by a spring k and damper c, and is subject to an external force f. At time t=0 the spring k is in its free length.
- . Derive the governing equations for this system in terms of the angular displacement of the pendulum ?(?), and the linear displacement of the cart ?(?).
- . Derive the expression for the tension force of the pendulum in terms of ?(?) and ?(?).
Image transcription text
M g
There exists a horizontal reaction force from the surfaces acting on the cart M that can be represented as a single force. Instead of representing the interaction force at the pivot as its horizontal and vertical components, consider a single tension force T of the pendulum. Instead of describing rotation of the pendulum about an accelerating pivot, consider only motion of its bob in the horizontal and vertical directions separately.
Physics
ISBN: 978-0077339685
2nd edition
Authors: Alan Giambattista, Betty Richardson, Robert Richardson