Hi Bruce, thanks so much for your help.
So I've found that the new resistance is R+α(2(L+x'cos(ωt))+l), and the EMF is -B'ωlx'sin(ωt). So I=V/R=-B'ωlx'sin(ωt)/(R+α(2(L+x'cos(ωt))+l)). This implies that V=IR=-B'ωlx'sin(ωt), which is the original EMF, not the answer given. Where am I going wrong?