A vertically suspended body with mass, M=12 kg is attached to the end of a spring that is stretched 0.098 m by the body. The body is also attached to a vertical dashpot that provides 2 N of resistance for 2 m/s velocity. It is set in motion from 1 m above
the equilibrium position with a downward velocity of 5 m/s.
Find the position function of the body as well as the damping condition, time-varying amplitude, natural frequency, and phase shift.

Ametal ring 4.20 cm in diameter is placed between the north and south poles of large magnets with the plane of its area perpendicular to the magnetic field. these magnets produce an initial uniform field of 1.12 t between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.240 t/s . (a) what is the magnitude of the electric field induced in the ring? (b) in which direction (clockwise or counterclockwise) does the current flow as viewed by someone on the south pole of the magnet?