What is a dynamic system

Dynamic system is a system that depends on past and future values to get the current output

Consider this system

Y(t)=X(t^2)

Here when t=-2 the output depends on the value of X at time t=4

Such a system is called Dynamic system

Is it clear now

Dynamic system-
It is the system whose output values are dependent on past and present values of input.
eg)- y(t) = x(t-2)
Let t=2 sec then output at 2 sec is equal to the input at 0 sec i.e. it is a delayer. Hence a dynamic system.
eg 2)- y(t)= x(t). Clearly the output at any time depends on the output at that time only, hence the system is not dynamic.

Time invariant system-
It is that system whose output is shifted by the same amount as the shift in input.
eg)- y(t) = x(t-2), now if the input is shifted by any amount, say x sec then the output will also correspondingly shift to x sec i.e. output is y(t-2-x) .
eg 2)- y(t) = x(t^2), now if the input is shifted to x, the output will be y(t) = x([t-x]^2), if the system would have been time invariant output would have been x(t^2 -x), hence the system is time variant.

I hope ur problem is solved now 😀

mifo

Dynamic system-
It is the system whose output values are dependent on past and present values of input.
eg)- y(t) = x(t-2)
Let t=2 sec then output at 2 sec is equal to the input at 0 sec i.e. it is a delayer. Hence a dynamic system.
eg 2)- y(t)= x(t). Clearly the output at any time depends on the output at that time only, hence the system is not dynamic.

Time invariant system-
It is that system whose output is shifted by the same amount as the shift in input.
eg)- y(t) = x(t-2), now if the input is shifted by any amount, say x sec then the output will also correspondingly shift to x sec i.e. output is y(t-2-x) .
eg 2)- y(t) = x(t^2), now if the input is shifted to x, the output will be y(t) = x([t-x]^2), if the system would have been time invariant output would have been x(t^2 -x), hence the system is time variant.

I hope ur problem is solved now 😀

can a dynamic system have its output dependent upon the past value of the output? What about future values of output? If the dynamic system's output is dependent on past values of input, then how is it going to be different from a non-causal system?

Dynamic system output can have both past and future values in the input section

proffy

can a dynamic system have its output dependent upon the past value of the output? What about future values of output? If the dynamic system's output is dependent on past values of input, then how is it going to be different from a non-causal system?

Since an R-C low pass filter is a dynamic(and causal) system and the expression for it's output(voltage) comes in the form involving integrals of input and output(you can try this yourself), so you can say that-

-) A dynamic system has it's output dependent on past,and future values alongwith the present values of input and output.
Whereas,

-) A causal system has it's output dependent on past and present input and output also.

Also you can say that a non dynamic system is a subset of causal system.