What are normal modes in a double spring system?

Normal modes are special patterns where both masses oscillate at the same frequency. The symmetric mode has both moving together at a lower frequency. The antisymmetric mode has them moving oppositely at a higher frequency. General motion is a mix of both.

Why does energy transfer between the two blocks?

When normal mode frequencies are different the two modes go in and out of phase creating beats. Energy appears to flow back and forth between the blocks. Set equal masses and no damping then pull only one block to see this clearly.

Double Spring Simulator — Coupled Oscillations

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