A special spring is constructed in which the restoring force is in the opposite direction to the displacement but is proportional to the cube of the displacement; i. e., F= -kx^3 this spring is placed on a horizontal frictionless surface. One end of the spring is fixed, and the other end is fastened to a mass M. The mass is moved so that the spring is stretched a distance A and then released. Determine each of the following in terms of k, A, and M
a) The potential energy in the spring at the instant the mass is released
b) the maximum speed of the mass
c) The displacement of the mass at the point where the potential energy of the spring and the kinetic energy of the mass are equal

Explanation:

a ) Restoring force in special spring F = k x³

let it is stretched by length l and it is further stretched by dl .

work done on spring in stretching by dl

= F dl

= k l³ dl

work done in stretching by A

= ∫k l³ dl between limit 0 to A

= k [ l⁴ / 4 ] between limit 0 to A

= k A⁴ / 4 ;

b )

Let v be the maximum speed attained ,

kinetic energy of mass = potential energy of spring

1/2 M v² = k A⁴ / 4

v² = kA⁴ / 2

v = A² √( k/2 )

c ) Let the required displacement be d .

potential energy = k d⁴ / 4

at displacement d , potential energy and kinetic energy are equal so potential energy = 1 /2 of total potential energy = 1/2 x k A⁴ / 4

= k A⁴ / 8

So

k A⁴ / 8  = k d⁴ / 4

science is a systematic and logical approach to discovering how things in the universe work. true to this definition, science aims for measurable results through testing and analysis. science is based on fact, not opinion or preferences. the process of science is designed to challenge ideas through research.

explanation:

i think if it were me i whould divide 300 dide 15

step-by-step explanation: