what the form equation of h(t) which make output y(t) if we have input x(t) ,h(t) is a linear time invariant system
thanks

 

Have you studied convolution in class?

 

Have you studied convolution in class?

no i did not

 

no i did not

but it will be taught in class

 

but it will be taught in class

can i solve it without using convolution

 

can i solve it without using convolution

Maybe someone else has a better idea, but you could write x(t) and y(t) in the time domain (in terms of t), take the Laplace transforms to get X(s) and Y(s), divide Y(s) by X(s) to get H(s), and then take the inverse of the Laplace transform to find h(t). After you go through that process, you'll find out why convolution is so nice to use in this case. Often times Laplace transforms are the best approach. Here I'm not so sure. I am assuming you've studied Laplace transforms, but maybe not.

One thing you might notice is that between t=0 and t=1, you effectively have an integration of a step input within h(t). Think about what is happening between t=1 and t=2 and for t>2.

 

Without knowing the context of the problem (i.e., why this problem was given and how it fits into the material before and after it), it is difficult to give a good answer. I think mlog has a good suggestion.

My first impression is that the response seems hinky. You apply a setp at t=0 and hold it constant until t=2s. In response, the output ramps up and ramps down in that same t=2s. If it is a linear time-invariant system, then if you shift the input pulse right (or left) by 2s, you shift the output the same amount. This means that if you applied a constant input of 1 for all time, that the output would oscillate in a triangular fashion between 0 and 2. That doesn't sound like a linear time-invariant system to me. But maybe I'm forgetting something simple.