In each of the questions below, hanging a mass m from a spring stretches the spring l meters from its unloaded length. calculate the spring constant k, write the differential equations that governs the motion of the undamped mass-spring system, and find the solution that satisfies the initial conditions specified. units are mks; the gravitational constant is 9.8 m/s2.

If a stone with an original velocity of 0 is falling from a ledgeand takes 8 seconds to hoybthe ground whays the final velocity of the stone

Amachinist turns the power on to a grinding wheel, at rest, at time t = 0 s. the wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 96 rad/s. the wheel is run at that angular velocity for 40 s and then power is shut off. the wheel slows down uniformly at 1.5 rad/s2 until the wheel stops. in this situation, the time interval of deceleration is closest to:

Scientists discovered fossils in several layers of the earth you see here. they found fossils of algae, snails, and clams in layer d. given that information, where do you think they found fossil evidence of simple land plants and amphibians?