The following information pertains to questions 1 and 2.

Three springs of the same relaxed length L_o have spring constants k₁ > k₂ > k₃. The springs are suspended from the ceiling and identical masses are then hung on each of the springs. In response to these identical stretching forces, the springs stretch amounts x₁, x₂ and x₃, respectively.

The elastic potential energies stored in each of the three springs are such that ___.

The following information pertains to questions 3 and 4.

The work required to stretch a relaxed spring with spring constant k_o an amount x_o is W_o.

The work required to stretch the relaxed spring an amount 3 x_o would be W_o x ___.

The following information pertains to questions 5-8.

A block with mass m_o on a horizontal, frictionless surface is tied to one end of a massless spring with spring constant k_o the other end of which is tied to a vertical wall. The block is pulled aside until the spring has been stretched an amount x_o, held at rest and released. When the block passes through its equilibrium position, its speed is v_o and its kinetic energy is KE_o.

If the initial stretch of the spring had been 2 x_o, the speed of the block as it passes through its equilibrium position would be v_o x ___.

If the spring had been stiffer, i.e., k > k_o, the speed of the block as it passed through its equilibrium position would have been ___ v_o.

If the mass of the block had been 4 m_o, the speed of the block as it passed through its equilibrium position would have been v_o x ___.

If the initial stretch of the spring had been 2 x_o, the kinetic energy of the block as it passed through its equilibrium position would have been KE = KE_o x ___.