TITLE:
On the Dynamics of Transition of a Classical System to Equilibrium State
AUTHORS:
Sami M. AL-Jaber
KEYWORDS:
Classical Oscillating System, Spring-Mass System with Friction, Energy Dissipation
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.8,
August
22,
2018
ABSTRACT: In this work we consider a spring with one end is fixed and the other is connected
to a block of mass M located on a horizontal rough table. The other
side of the block is connected to a massless rope that passes over a frictionless
pulley at the end of the table and a second block of mass m is hanged at the
rope’s other end. For this system, we analyze and discuss its dynamics of motion
as function of time when the second block is released. In particular, the
displacement of the system at the end of each half-cycle of motion, the total
distance, and the work done against friction are derived. An interesting result
is obtained for the case when the table is frictionless. It is found that there is
still a work done by friction whose magnitude is exactly the same as the
stored energy in the spring.