$$A$$ and $$B$$ are two fixed points at a distance $$3l$$ apart. A particle of mass $$m$$ placed at a point $$P$$ experiences the force $$2(mg/l)PA$$ and the force $$(mg/l)PB$$ simultaneously. Initially at $$t=0$$ the particle is projected from $$A$$ towards $$B$$ with speed $$3\sqrt{gl}$$
The particle moving simple harmonically with period $$T$$ and amplitude $$A$$