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Step 1: Circuit diagram

Picture of Circuit diagram
Each coil is placed in series with a diode and three of these configurations in parallel. This way when one coil is providing energy, that power will not be consumed by the two other coils (simple half wave rectifier). The current flows directly to the LEDs where the voltage is the one generated by the coil with about 0.6V drop at the diode in case of a general purpose one. For a schottky it should drop only 0.3V or even less.

When the capacitor is connected to the circuit, it will be charged and will keep the LEDs on for some time when no coil is providing power.