running AC synchronous motor with DC
Use your AVR to modulate the pulse widths to mimic a sinewave instead of just hitting the motor with high-low pulses: -


(source: smps.us)  

The PWM frequency you choose (maybe 1kHz or higher) may still cause a little noise but this is more easily filtered: -



The resonant frequency of the filter will need to be lower than your pwm switching frequency and higher than the ac frequency you are trying to smoothly reconstruct so if your pwm frequency is 1kHz and you want 70Hz to be reconstructed, choose a frequency for resonance that is logarithmically half way between the two ends (\$\sqrt{F_{SYNC}\cdot F_{PWM}}\$).

Resonance is at \$\dfrac{1}{2\pi\sqrt{LC}}\$