A rod of length l and mass m, pivoted at one end, is held by a spring at its midpoint and a spring at its far end, both pulling in opposite directions. The springs have force constant k, and at equilibrium their pull is perpendicular to the rod. Find the frequency of small oscillations about the equilibrium position.

An astronaut in space cannot use a scale or balance to weigh objects because there is no gravity. but she does have devices to measure distance and time accurately. she knows her own mass is 77.4 kg , but she is unsure of the mass of a large gas canister in the airless rocket. when this canister is approaching her at 3.50 m/s , she pushes against it, which slows it down to 1.30 m/s (but does not reverse it) and gives her a speed of 2.60 m/s . what is the mass of the canister?