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DOMV No 2 RESPONSE OF LINEAR SDOF SYSTEMS TO GENERAL LOADING (2).pdf
1. Response of linear SDOF systems to general
loading â use of superposition.
Mass-Spring Damper System
y is the displacement, in the downward direction, as
a result of the force p(t) acting on m
p(t)
k c
m
y
2. An approach to constructing the
general solution for arbitrary forcing
3. Linear systems satisfy the principle of superposition
(in the Time and Frequency Domains)
?
10. Impulse response
Mass-Spring Damper System
Consider a unit impulse h(t) applied to a mass-
spring-damper system, with light (subcritical)
damping parameter Ο (i.e. Ο << 1) and natural
frequency Ïn . How would it respond?
h(t)
2ΟÏn
y
12. To recap
Two functions have been defined: the Unit
Amplitude Free Decay Function:
đŠ(đĄ) = đŠUAFD(đĄ)
and the Impulse Response Function h(t) (which
is identical to the Unit Velocity Free Decay
Function):
đŠ đĄ = h t = đŠUVFD đĄ
We will see in the next lecture that only these two
functions are needed to generate the general solution
to the forced response of a SDOF system.