The phenomenon of large values for the amplitude of oscillation is known as resonance.
4. Coupled Oscillations
Consider two masses \(m_1\) and \(m_2\) on a frictionless horizontal plane, attached to each other by a spring with spring constant \(k\). Let \(x_{1}\) and \(x_2\) be the displacement of the masses from their respective reference positions when the spring is unstretched. Note that we are assuming only one-dimensional motion of the masses in the longitudinal direction (along the line of the spring).
4.1 Write down the equations of motion for both masses. Be extremely careful with direction.