I'll review the perturbative formalism to quantum quenches near a quantum critical point in 1+1 dimensions introduced in [1]. I'll then provide explict applications of it to the Ising and the XYZ spin chain. I will finally argue how the mass spectrum of a theory can be inferred from quantum dynamical experiments and Fourier analysis: these considerations notably apply to the spectrum of Ising field theory in a magnetic field (Zamolodchikov "E8" spectrum).