Two springs and two masses are attached in a straight line on a horizontal frictionless surface as illustrated in the figure to the right. The system is set in motion by holding the mass m2 at its equilibrium position and pulling the mass m1 to the left of its equilibrium position a distance 1 m and then releasing both masses. Express Newton's law for the system and determine the equations of motion for the two masses if m1 = 1 kg, m2 = 2 kg, k1 = 3 N/m, and k2 = 7/2 N/m.
Express Newton's law for the system. Write expressions in terms of x, y, k1, and k2.
m1x'' = k1(y - x)
m2y'' = -k1(y - x) - k2y
Determine the equations of motion for the two masses.
x(t) =
y(t) =