I guess your DC motor is brush-type? Then it has numerous coils of wire wound on an armature. Each coil's impedance is some portion ohmic resistance and some portion inductance (Henry value). You can read ohmic resistance with an ohmmeter. Inductance is measured with more sophisticated equipment.
The waveform through the motor is sort of like a switched-coil converter. Say you have 20 coils going at 10 rps (=600 rpm). Each coil receives voltage for 1/200 second. In that time the coil draws 120 Watts average. Calculate the RL time constant which yields that response, to get an idea of Henry value.
There's the observation that a motor draws greater current at slower speeds. At first it seems unexpected, although it makes sense when we realize more current flows in an inductor the longer voltage is applied.