If a particle moves with acceleration = #10x2x^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]}