ECE 205 - Winter 2017
Assignment 3 Solutions
is the first derivative of the position with respect to time and ¨
is the second derivative of
the position with respect to time.
What choices for
oscillations? In this regime, what is the angular
frequency of oscillations?
If the value of
is chosen such that the system is on the boundary of being
then we say that the system is critically damped. Suppose that the system is critically damped,
and we have the initial values
(0) = 1 and ˙
the particular solution solving this
IVP in terms of
that no matter what the initial velocity
is, the mass can never pass
the equilibrium point more than once.
4: Almost Simple Harmonic Oscillator
Consider the ODE
) + 2
) = 0
How many oscillations take place until the amplitude decays by 1% when: