A mass, m, is attached to a support by a spring with spring constant, k. The mass is hanging down from the spring, so there is a gravitational force on the mass as well. Neglect any resistive or frictional force. The support is then oscillated with an amplitude of A and at a frequency of ωa .
a) Find the motion of the mass relative to the support.
b) Find the motion of the mass relative to the lab (inertial frame).
The Attempt at a Solution
I found the motion of the mass relative to the support to be
by integrating twice
which seems reasonable.
For part b, I said
so the motion of the mass relative to the lab
Is this valid?