The most common dissipation process is friction, but you cannot obtain an analytic solution for the harmonic oscillator with frictional loss. However, consider the case for which the frictional loss/period is small \((\Delta E/E << 1)\) .
Obtain an approximate solution for this case. Sketch your solution E(t) and compare the result with the usual damped oscillator solution. The oscillator has mass m, spring k, and constant friction force Fo. (You may find it helpful to write a differential equation for the energy E(t) of the oscillator.)