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Unformatted text preview: to Eq. 2.16 we will have:
= / = and = (ii) The variable ωn denotes the natural frequency of the spring damper system. Show
that the natural frequency ωn can be increased by increasing the value of the spring
constant k or by decreasing the mass M.
/ we can see that increasing k increases ωn, or decreasing M.
(iii) Determine whether the system is
3 + = 1 + + 2 3 + 1 so =1
3 =[ +
The system is linear. and + + 1 2 + 3 + + So y1(τ)=y(τ-t0)
The system is time-invariant.
(c) memoryless 1 τ+ 0 3 = 1+ [ (b) time-invariant
For x(t-t0) applied as the input, the output y1(t) is:
Substitute τ=t-t0 so dt=dτ
1 τ+ 0
+ + + 1
2 + 2 + =2 2 2 =
1 τ+ 0 = +0 EE 341 Fall 2012
To get the output we need to integrate twice the second order diff. eqn.
It is clear that the output depends on past values of the input.
System is not memoryless. (d) causal
From part © we can deduce that the system is causal
x(t) can be obtained from equation above so system is invertible.
The system is BIBO.
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- Fall '09