An　optomechanical　cavity　driven　by　a　periodically　amplitude-modulated　laser　can　generate　steady　light-mechanical　entanglement　with　time　periodicity.　Similar　results　can　be　alternatively　obtained　by　pumping　an　especially　tuned　optical　degenerate　parametric　amplifier　(DPA)　inside　the　cavity.　While　the　two　laser　beams　are　simultaneously　applied,　the　optomechanical　entanglement　can　exhibit　constructive　and　destructive　interference　patterns,　depending　on　their　cooperative　phase,　which　further　gives　rise　to　beating　in　entanglement　dynamics　if　the　two　modulation　frequencies　are　slightly　different,　followed　by　a　beating　frequency-dependent　dynamical　behavior　in　the　energy　exchange　between　light　and　a　mechanical　oscillator.　The　optimal　dynamical　entanglement　goes　beyond　what　is　attainable　by　the　scenario　with　two　superimposed　cavity　drivings,　as　a　result　of　the　specially　DPA-modulated　quantum　dynamics.　Moreover,　we　calculate　correlation　spectra　between　the　cavity　and　mechanical　modes,　and　we　find　correspondence　between　the　light-oscillator　entanglement　and　the　correlation　spectra　under　the　cooperative　effect.　The　cooperation-enhanced　optomechanical　entanglement　is　robust　against　the　thermal　temperature,　and　is　potentially　useful　for　continuous　variable　quantum　information　processing.　©　2020　American　Physical　Society.