A cart of mass 1.5 kg is attached to two horizontal ideal springs that are connected in series between the cart and a rigid wall. Spring A has a force constant of 200 N/m and Spring B has a force constant of 300 N/m. The cart rests on a frictionless surface.
(a) Determine the single spring constant that could replace the two-spring combination without changing the mechanical behavior of the system.
(b) If the cart is pulled 0.10 m from its equilibrium position and released from rest, calculate the period of the resulting small oscillations.