Simplify these expressions: (a) cos(πt)(δ(t) + δ(t − 1)) (b) Z [infinity] −[infinity] cos(πt)(δ(t) + δ(t − 1))dt (c) Z [infinity] −[infinity] f(t + 1)δ(t − 2) dt (d) Z [infinity] −[infinity] e jωT δ(t) dt (e) Z [infinity] −[infinity] f(τ )δ(t − 1)δ(t − τ )dτ

Describe one experiment in which the glass transition temperature and melting temperature of a totally amorphous thermoplastic material can be determined. show the relevant experimental results in a diagram which should be properly annotated with the two temperatures clearly marked. what is likely to happen to the curve in the diagram if the amorphous polymer is replaced by a thermosetting type?