Question

in a certain ,the potential energy is U=ax² -bx³,where a and b are constant .the particle is in stable equilibrium at x equal to 0​

Answer 1

Answer:

a should be + ve

Explanation:

In a certain ,the potential energy is U=ax² -bx³,where a and b are constant .the particle is in stable equilibrium at x equal to 0​

U=ax² -bx³

=> dU/dx = 2ax - 3bx²

to find minima or maxima point

dU/dx = 0

=>  2ax - 3bx² = 0

=> x = 2a/3b  or x = 0

d²U/dx² =  2a - 6bx  

for x = 0 d²U/dx² = 2a  => 2a should be + ve as x = 0 is minimum energy

putting x = 2a/3b

d²U/dx² = 2a - 6b*2a/3b   = -2a    => a should be + ve