Determine whether each of the following LTIC systems is i) BIBO stable, ii) asymptotically stable, and iii) marginally stable. E
xplain why or why not. (a) d 3y dt3 − 3 dy dt − 2y(t) = df dt − f(t) (b) d 3y dt3 − 3 dy dt − 2y(t) = df dt − 2f(t) (c) d 2y dt2 + 3 dy dt + 2y(t) = df dt + f(t) (d) d 2y dt2 + 2 dy dt + 2y(t) = f(t) (e) d 2y dt2 + 2y(t) = f(t)
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We know that speed (rate) is equal to distance over time.
The current unit of distance is miles, and we want to convert it to feet. The unit of time is hours, and we want seconds. In order to do this, we need to create a conversion factor.
Since
and 
, we will use these are our conversion factors.
The goal in a dimensional analysis problem like this is for your units to work out. Remember, we want feet per second.
We write
.
You may wonder why in the conversion factor, we chose to put feet over miles and hours over seconds. This is again because we want our units to cancel. If you have one unit the numerator and the same one in the denominator, the units cancel out.
In sum, the answer is 22 ft/s.
The current unit of distance is miles, and we want to convert it to feet. The unit of time is hours, and we want seconds. In order to do this, we need to create a conversion factor.
Since
The goal in a dimensional analysis problem like this is for your units to work out. Remember, we want feet per second.
We write
You may wonder why in the conversion factor, we chose to put feet over miles and hours over seconds. This is again because we want our units to cancel. If you have one unit the numerator and the same one in the denominator, the units cancel out.
In sum, the answer is 22 ft/s.
Step-by-step explanation:
Cross Multiplying
Therefore
Hope it will help you.