<p>In this article, we present the mechanics of an oscillator that is subject to a restoring force that is constant, independent of the position of the oscillator. Both classical and quantum mechanics are presented. Comparison with the simple harmonic oscillator is made in each case. We also present the momentum eigenfunctions of the oscillator and derive orthogonality relation of the Airy function which is the solution of Schrödinger equation for this system. One may note that the system is not normally presented in the physics literature. However, like the simple harmonic oscillator, the system can be used to illustrate the fundamental concepts of both classical and quantum mechanics. Further, we usually use the boundary conditions on the wavefunction to obtain the eigenfunctions and eigenenergies. In the case of a linear oscillator here, we illustrate the use of the symmetry requirement on the wavefunction to quantize the system.</p>