a. A body of mass m suspended on a spring oscillates such that the greatest value of velocity is v₀, and the greatest deviation from the equilibrium position is x₀. Determine the stiffness of the spring.
b. The velocity of a body of mass m suspended on a spring and oscillating depends on the coordinate of the body x according to the law v = v₀√(1−(x/x₀)²). Find the relation between the force acting on the body and the potential energy of the body and the coordinate x. Does the result depend on the nature of the force that makes the body move according to the above law?