Question

The potential energy of a particle moving along the x-axis is given by U(x) = 8x2 + 2x4, where
and x is in meters. If the total mechanical energy is 9.0 J, the limits of motion are
(1) -0.96 m. +0.96 m
(2) -2.2 m, +2.2 m
(3) -1.6 m, +1.6 m
(4) -0.96 m, +2.2 m
(5) -0.96 m, +1.6 m​

Answer 1

Explanation:

the turning points of an oscillator occur when its KE is zero, meaning when all of its energy is in the form of potential

therefore, we have

U(x) = 9.0J = 8x^2 + 2 x^4

or when 2 x^4 + 8 x^2 -9=0

this is a quadratic equation in x^2 (to see this, set u = x^2 and get

2u^2 +8u-9=0 )

solving this for u yields u=0.915 and u=-4.92