A block moves on a spring whose potential energy is fixed in the ground frame

PHYSICS · Subjective · Fermi University Physics · Mechanics & Dynamical Systems · Lagrangian mechanics · Lagrangian mechanics

Action and Symmetry, Ch Symmetry, Noether's theorem and what is conserved

Problem

A block moves on a spring whose potential energy

V(x)=\tfrac12 kx^2

is fixed in the ground frame, so for this system the Jacobi integral equals the mechanical energy,

h=E

. The block also experiences linear drag represented by the Rayleigh dissipation function

\mathcal F=\tfrac12 b\dot x^2

with

b=0.15\ \mathrm{kg\,s^{-1}}

. At an instant when the block's speed is

0.80\ \mathrm{m\,s^{-1}}

, find the rate at which

h

is changing.