This paper presents an analysis of a periodically forced piecewise linear oscillator, which models mechanical systems with intermittent contact. The system is described by a second-order differential equation with a piecewise linear restoring force. The nonlinearity is characterized by a single change in slope, and the system can be analyzed using both analytical and numerical methods. The paper investigates the existence of harmonic, subharmonic, and chaotic motions, as well as the bifurcations that lead to these behaviors. The system is analyzed in two main cases: the general case with a finite stiffness and the impact limit where one stiffness approaches infinity. In the general case, the system is governed by a differential equation with a piecewise linear restoring force, and the solutions are derived using a combination of analytical and numerical techniques. The paper introduces the concept of a Poincaré section and a return map to study the system's behavior, particularly focusing on periodic orbits and their stability. In the impact limit, the system becomes an impact oscillator, where the restoring force is modeled by a linear spring with a very high stiffness. The paper derives the equations of motion for this system and analyzes the behavior of periodic orbits, including single-impact and multiple-impact orbits. The analysis shows that the system can exhibit period-doubling bifurcations, leading to chaotic motions. The paper also discusses the stability of periodic orbits and the bifurcations that occur as system parameters are varied. It presents analytical results for the impact limit and compares them with numerical simulations. The analysis shows that the system can exhibit a wide range of behaviors, including stable and unstable periodic orbits, as well as chaotic motions. The paper concludes that the system is a useful model for understanding the behavior of nonlinear oscillators with intermittent contact.This paper presents an analysis of a periodically forced piecewise linear oscillator, which models mechanical systems with intermittent contact. The system is described by a second-order differential equation with a piecewise linear restoring force. The nonlinearity is characterized by a single change in slope, and the system can be analyzed using both analytical and numerical methods. The paper investigates the existence of harmonic, subharmonic, and chaotic motions, as well as the bifurcations that lead to these behaviors. The system is analyzed in two main cases: the general case with a finite stiffness and the impact limit where one stiffness approaches infinity. In the general case, the system is governed by a differential equation with a piecewise linear restoring force, and the solutions are derived using a combination of analytical and numerical techniques. The paper introduces the concept of a Poincaré section and a return map to study the system's behavior, particularly focusing on periodic orbits and their stability. In the impact limit, the system becomes an impact oscillator, where the restoring force is modeled by a linear spring with a very high stiffness. The paper derives the equations of motion for this system and analyzes the behavior of periodic orbits, including single-impact and multiple-impact orbits. The analysis shows that the system can exhibit period-doubling bifurcations, leading to chaotic motions. The paper also discusses the stability of periodic orbits and the bifurcations that occur as system parameters are varied. It presents analytical results for the impact limit and compares them with numerical simulations. The analysis shows that the system can exhibit a wide range of behaviors, including stable and unstable periodic orbits, as well as chaotic motions. The paper concludes that the system is a useful model for understanding the behavior of nonlinear oscillators with intermittent contact.