Mechanisms under which a sequence converges weakly in $L^p$ spaces

Question

I'm studying the book Analysis, by Lieb and Loss, and trying to prove what they call the heuristic ways, under which a sequence of function converges weakly in $L^{p}(\mathbb{R})$.
1. $f_{n}(x)=\sin(nx)$
2. $f_{n}(x)=n^{1/p}g(nx)$
3.$f_n(x)=g(x+n)$
My attempts are sketchy, 1, basically follows from the Riemann-Lebesgue Lemma, the second, I think, by a simple change of variable $y=nx$ then canging the power of $n$ to become $-1/q$, but no idea how to deal with the third one, or indeed make any of my proofs rigorous.