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ASEN 5519 Nonlinear Mechanical Vibrations
Homework 1 (Due Tue. February 8, 2022)
PROBLMES
Problem 1
Consider a viscously damped SDOF spring-mass oscillator, described by the EOM
,
and subject to the following initial conditions:
Derive the response x(t) for the overdamped case, where
,1
in terms of x0 and v0 and in
terms of exponential functions. Note, in class you were given an alternative final form of the
solution for this problem in terms of a hyperbolic sine function.
Show your derivations in detail.
Problem 2
The spring-mass oscillator in the figure has a velocity-feedback force generator that exerts a
force fv on the mass that is proportional to the velocity of the mass. The sign of the force can
be either positive or negative. For a particular setup of this SDPF system, the spring, mass,
and feedback force parameters lead to the following differential equation of motion:
,
where u is the displacement of the mass in inches (this is equivalent to the “x” we use in class.
(a) If the initial conditions are
determine the motion function u(t).
(b) Using your answer to part (a), write a computer code (a Matlab m-file) and obtain a plot
of the solution.
