Consider four different oscillating systems, indexed using $i=1,2,3,4.$ Each system consists of a block of mass $m_i$ moving at speed $v_i$ on the same frictionless surface while attached to an ideal, horizontal spring with a force constant of $k_i$ that is fixed at its other end.

Let $x$ denote the displacement of the block from its equilibrium position and A denote the maximum oscillation amplitude. Order the systems from largest total mechanical energy to smallest.

Assume that the surface defines the zero reference point for gravitational potential energy.

Smallest total mechanical energy

Answer Bank

$m_1=0\mathrm{.}50kg$;$k_1=500\frac{N}{m}$; amplitude $A=0\mathrm{.}020m$

$m_2=0\mathrm{.}60kg$;$k_2=300\frac{N}{m}$;$v_2=1\mathrm{.}0\frac{m}{s}$ when passing through equilibrium

$m_3=1\mathrm{.}2kg$;$k_3=400\frac{N}{m}$;$v_3=0\mathrm{.}50\frac{m}{s}$ when passing through $x=-0\mathrm{.}010m$