(I) (a) What is the equation describing the motion of a mass on the end of a spring which is stretched 7.8 cm from equilibrium and then released from rest, and whose period is 0.66 s?
(b) What will be its displacement after 1.8 s?

A 280-kg wooden raft floats on a lake. When a 68-kg man stands on the raft, it sinks 3.5 cm deeper into the water. When he steps off, the raft oscillates for a while.

(a) What is the frequency of oscillation?

(II) A 0.350-kg mass oscillates on the end of a thin vertical spring (spring constant 265 N/m) with an amplitude of 28.0 cm. The mass passes through the equilibrium point (y = 0) with positive velocity at t = 0 .

(a) What equation describes this motion as a function of time?

A 62-kg person jumps from a window to a fire net 20.0 m directly below, which stretches the net 1.4 m. Assume that the net behaves like a simple spring.

(a) Calculate how much it would stretch if the same person were lying in it.

A particular unbalanced wheel of a car shakes when the car moves at 90.0 km/h. The wheel plus tire has mass 17.0 kg and diameter 0.58 m. By how much will the springs of this car compress when it is loaded with 280 kg? (Assume the 280 kg is split evenly among all four springs, which are identical.)

A 62-kg person jumps from a window to a fire net 20.0 m directly below, which stretches the net 1.4 m. Assume that the net behaves like a simple spring.

(b) How much would it stretch if the person jumped from 38 m?

(II) A 0.350-kg mass oscillates on the end of a thin vertical spring (spring constant 265 N/m) with an amplitude of 28.0 cm. The mass passes through the equilibrium point (y = 0) with positive velocity at t = 0 .

(b) At what times will the length of the spring be longest and shortest?

(II) A 1.60-kg object oscillates at the end of a vertically hanging light spring once every 0.68 s. . Assume the spring was initially compressed 16 cm from the equilibrium position (where y = 0 ), and then (t = 0) was released.

(d) What will be its maximum acceleration, and where will it first be attained?

(II) A wood block of mass 52 g floats on a lake, bobbing up and down at a frequency of 3.5 Hz.

(b) A partially filled water bottle of mass 0.28 kg and almost the same size and shape of the wood block is tossed into the water. At what frequency would you expect the bottle to bob up and down? Assume SHM.