We discuss the properties of pulsations in the OGLE Small Amplitude Red Giants ( OSARGs ) in the Large Magellanic Cloud ( LMC ) . We consider stars below the red-giant tip in this paper . They are multi-periodic and form three sequences in the period-luminosity plane . Comparing the periods and period ratios with our theoretical models , we have found that these sequences correspond to radial first to third overtones , and nonradial dipole p _ { 4 } and quadrupole p _ { 2 } modes . The red-giant branch stars of OSARGs consist of stars have initial masses of \sim 0.9 - 1.4 M _ { \odot } which corresponds to a luminosity range of \log L / L _ { \odot } \simeq 2.8 - 3.4 . With these parameters , the scaled optimal frequency \nu _ { max } for solar-like oscillations goes through roughly the middle of the three sequences in the period-luminosity plane , suggesting the stochastic excitation is likely the cause of the pulsations in OSARGs .