My question may be very basic or childish but this question still persists in m

My question may be very basic or childish but this question
still persists in me, someone plz help me
1.why do we go for differential equations to analyze a system?
2.why do we solve it using matrices, is there any specific
reason for using matrices other than the stories like it is
simple,faster etc.

Question Posted / prashanth

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My question may be very basic or childish but this question still persists in me, someone plz help ..

Answer / h v k kumar,mtech,instrumentat

if u model the any system like
mmechnical/electrical/pneumatic establish relation b/w
input and o/p force,mass,friction etc a=dv/dt,f=m(dv/dt)
model all forces and adding all forces we get diff equation
homo/non hom solve by using laplace trnsformation.but here
initial conditions assumed to be zero solution is state
space analysis using matlab ,so matlab variables are
arrngend matrix format.

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My question may be very basic or childish but this question still persists in me, someone plz help ..

Answer / jobby c johnson

in continous domain inorder to analyse the system dynamics
we are going for differantial equation. simillarlly in
discrete domain we are going for differance
equation.because discrete domain is the sampled version of
analog system. now the differantial euation may be
homogenous(ie we are not applying any input) then the
response what we are getting shows how the system acquires
or desiipates energy. if the differantial equation is
nonhomogenous system then the response shows how the output
follows the input. once you got the differantial equation
either by laplace transform or by z transform u can analyse
the system

the problem in this type of analysing is that we are not
considering initial conditions and also it is no good for
mimo modelling. so we are going for state space design or
moder control