Amass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. starting at t 0, an external force equal to (t)-4 sin(4t) is applied to the system. find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (use g = 32 ft/s* for the acceleration due to gravity.)

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?