Causality problem

Hi all,

Can someone please guide me on how to determine if y(t) = e^-t cos(2ωt) is causal , where x(t) is cos(2ωt).

Am I correct if I say that first you have to select a negative value for t and then a positive value?

What value should I use for ω?

Any help would be highly appreciate.
Thanks.

i have another three questions:

1) Am I correct if I say that the output of the system below is dependent on two inputs?

y(t) = x(t-3) + x(3-t)

2) To check for causality, do I have to consider input x(t) only? For instance, in the system below, do I ignore cos(2t) ?

y(t) = cos(2t) x(3-t)

3) For y(t) = x^2(2-t) , since the input is not in the form of x(t) but x^2(t), is there another method of how to determine if the system is causal or not?

Thanks in advance for the help.

Any suggestions on these please?

Causal systems don't depend on future values. If you can find any violation of this it is not a causal system,

Take the example y(t)=x(3-t). If t=1. Then y(1)=x(2) which means that the present value of y depends on future values of x, and hence this is not a causal system.