A system may or may not be:

1.) Memoryless
2.) Time Invariant
3.) Linear
4.) Casual
5.) Stable
Determine which of these properties hold and which do not hold for each of the following continuous-time systems. Justify your answers. In each example, y(t) denotes the system output and x(t) is the system input.

a.) y(t)=x(t-2)=x(2-t)
b.) y(t)=[cos(3t)]x(t)
c.) y(t)=\int2t-infinity(x(?t)dt
d.) y(t)=0 for t<0 & x(t)+x(t-2) for t>or=0
e.) y(t)=0 for x(t)<0 & x(t)+x(t-2) for x(t)>or=0
f.) y(t)=x(t/3)
g.) y(t)=dx(t)/dt

During the experiment if you could triple the breakaway magnetic force with all other quantities left unchanged, what is the new value for the critical velocity if it was v0 (initial velocity), initially? (b) now if you halved the radius with all other quantities left unchanged, what is the new critical velocity if it was v0 (initial velocity), initially? (c) if during the experiment, critical velocity quadrupled with all other quantities left unchanged, what is the new breakaway force if its magnitude was initially f0,?