If a particle moves with acceleration = #10x-2x^3# and v= 0 at x=1, is the motion simple harmonic? And how do you describe the motion?
1 Answer
This is not SHM, because SHM requires a linear restorative force, ie SHM would require an acceleration in the form:
#a = - k x#
The potential function
For
graph{-5x^2+x^4/2 [-5, 5, -15, 10]}
We are told that
Also:
-
#V(1) = - 4.5# -
#V(3) = - 4.5#
The particle will thetefore oscillate back and forward in
This is a stable equilibrium.
Phase Portrait
Integrating wrt
The graph of
graph{y^2 = 10x^2- x^4 - 9 [-3.5, 3.5, -10, 10]}