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Homework Statement
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).
Homework Equations
F=ma
The Attempt at a Solution
I found the motion of the mass relative to the support to be
x*=-kAcos(ωt)/(mt^2)-(gt^2)/2
by integrating twice
ma*=kAcos(ωt)-mg
which seems reasonable.
For part b, I said
x=x*+Acos(ωt)
so the motion of the mass relative to the lab
x=Acos(ωt)(1-k/(mt^2))-(gt^2)/2.
Is this valid?