2. A spring with negligible mass, spring constant k, and relaxed length $l_0$ is suspended
from the ceiling, with a small mass m attached to its end. The size of the mass in this
problem is negligible compared to other length scales. The mass initially rests on the
table placed at a distance h below the ceiling, with part of its weight supported by the
spring, and part by the table.
(a). Sketch the force diagram for the mass, and determine the normal force exerted by the
mass on the table, in terms of the given quantities. What is the constraint on h so that the
mass rests on the table and is not hanging entirely on the spring?
h
(b) At time $t_0$=0, the table is quickly removed from under the mass, without perturbing it, and the mass
subsequently experiences oscillations with negligible damping. Determine the distance d(t) between the
mass and the ceiling as a function of time. Advice: as an intermediate step, it is useful to determine the
distance $d_0$ between the mass and the ceiling in equilibrium, after the oscillations die out. The oscillations
occur around this equilibrium position.
