Consider mass M hanging on a massless vertical spring with
spring constant k. The mass is at rest. At t = 0 a piece of
the mass falls off, leaving only a fraction α of the original
mass attached to the spring. Gravitational acceleration is g .
Assume that the mass moves along the vertical y – axis. At t
= 0 the mass was at y = 0.
a) Find the new equilibrium position as a function of the given
parameters.
b) The mass will oscillate. What is the period of the
oscillations?
c) What is the time dependence of the vertical position, y (t) ?
To answer this question choose the new equilibrium position (i. e.
the equilibrium position of mass αM ) as a new origin on the
y-axis.
d) What are the amplitude and phase at origin of time of the
motion in terms of the given parameters?
e) What is the kinetic and potential energy of the oscillating
system as a function of time?
f) What about the mechanical energy of the oscillator?