A new echo phenomenon in proteins, a generalization of so-called temperature quench echoes, is introduced and shown to reveal, through molecular dynamics simulations, periodic motions (normal modes) in proteins with phase coherence times of about one picosecond. The echoes are induced through reassignments of Cartesian velocities to protein atoms at times t = 0 and t = tau(0 < tau less than or equal to 1 ps) and appear as two sharp (widths of about 5 fs) features in the kinetic and potential energy at t = 3 pi/2 and t = 2 tau. The velocities, assigned at t = 0 and at t = tau to each atom, need to be correlated, but can otherwise be random. The echo at 3 tau/2 can be induced without any change in the temperature of the protein. Skeletal motions involving angular and stretch motions contribute principally to the echo effect. Electrostatic interactions do not affect the echoes. The echoes in the temperature are described, in the framework of the harmonic approximation, in terms of the equilibrium temperature-temperature correlation function. The velocity reassignments induce the echoes through the generation of phase coherence of protein modes. Phase relaxation due to anharmonic interactions, lead to a dependence of the echo depths on the time interval tau between velocity replacements which can be accounted for by phase diffusion or by Langevin oscillators. The echo effect can provide a sensitive probe for the study of non-diffusive energy transport in proteins.