Since we had power outages on and off since Sunday, because of the winter storms and as ERCOT (Electric Reliability Council of Texas) is asking utility distributors like CenterPoint Energy, Entergy, and etc. of disconnecting customers from the grid, because of low grid capacity from its electric plants. So as we had a power outage yesterday night, I looked at the voltage of the generator that is putting out which is 120V with a frequency of 61.06Hz, I tried my air cleaner on it and it sounded HORRID!  So IDK is it good to put magnetic inductive loads like electric motors and magnetic & electronic lighting ballasts on a generator?

It’s probably fine. Just watch the current draw and temperature of the motor or ballast.

The horrible noise came from where?
The engine?
Loaded engine will make way distinct engine than the one just nearly free running, so it could be normal (throttle opening means higher pressures, both during compression, but as well at the end of the expansion cycle, when the opening of the exhaust valve causes the gasses to rush out still at pressure so creating a loud "boom").
Many generators have huge label showing the peak power capability. But only hidden within the manual is some tiny note than you may load it to the max peak power only for few minutes. The problems usually are the thermal management and lubrication not being adequately designed for such high load.
The thing relies only on thermal inertia to sustain the peak loads. And consider the accelerated wear at that high load as acceptable when it is supposed to be loaded that way only for short times.

As long as the genset has a high enough VA rating it would work. Bear in mind that they don't regulate the frequency as well as the AC mains but is pretty close. The VA is crucial not the wattage. A 2.4kw welder could draw 4.8kVa and using a 2.4Kw genset won't work as the welder is drawing more current due to power factor. Electronic gear shouldn't care as some of them rectify the mains anyway so you could essentially run it off DC. 61Hz shouldn't harm anything for a short amount of time like a power cut.

The VA is crucial not the wattage.

Not correct, both are critical, but each is affecting different part.
Too high VA may overheat the generator,
too high Watts overload the combustion engine, so it may overheat (and seize because the oil loses lubrication ability when too hot) or prematurely wear out (may start knocking - detonation style combustion; the engine wears really fast in that mode, if too severe, the engine can throw a rod in matter of minutes), or cause excessive CO emission and soot buildup (when the carburetor is made to highly enrich the mixture at high loading, in an attempt to prevent the knocking; plus it drains the fuel pretty fast then; it is designed to just cover dynamic loads in that mode).

The generators can put out "dirty" power with fluctuations. I ran a fan on it once and you could hear the air movement change going up and down vs steady on regular AC power.

I would run anything on a generator through a surge protector, but that just my thoughts on it.

The generators can put out "dirty" power with fluctuations. I ran a fan on it once and you could hear the air movement change going up and down vs steady on regular AC power.

The generator can not make its output dirty on its own. To the contrary, hf-wise the output is way cleaner than the mains.
But it has rather high impedance, mainly at higher frequencies (harmonics), so a dirty load can make the generator voltage more dirty than the mains.
Mainly cheap generators are weak in this aspect. They are build with an expectation they would be used with just a single device as a load and there is an assumption the load is either clean, so wont disturb the voltage (radio,...), or tolerant towards the disturbances (e.g. power tools).
Definitely the fan is a clean load by itself (there is nothing to upset the voltage, it just has its impedance), so I doubt it could be part of the cause. The fan is sensitive on the voltage and mainly frequency fluctuacions, but these then must originate from the generator itself.


That fluctuating fan sounds to me like the engine rpm governor is oscillating (hunting; if it sees too low rpm, it takes it too long to correct the power and then it overreacts, causing the rpm to overshoot and then the same in the opposite direction), normally there is no reason why the fan should fluctuate at all.
The cause could be wear of the linkages so there is a significant play in actuating the throttle.
Or the joints and bearings are dirty so exhibit friction, creating a hysteresis. Mainly when the friction exceeds the tension of the linkage slack eliminating springs.
Or unstable operation of the engine itself (unstable mixture, clogged air filter, dirty air passages, sticky float valve, obstruction in the fuel feed, incorrectly operating choke, weak ignition, dirty, overheating or failing spark plug, dirty combustion compartment, loose magneto assembly, misaligned ignition timing, sticky internal engine components because the oil was not changed as it should be).
Or combination of all.

Dont feel bad I was In Same Boat in SpringBranch, Tx
 I had act like Ercot around my house to ballance my load
  As I dont have a charge Controller.  Meaning i contantly have to watch the the Loads make sure i stay around 13.8 volts
  Meaning had uncontrolled power source.  A junk 12 volt car battery from a scrap yard.  I have 1200 watt inverter 2400 watt peak.   2100 watts of solar power.  I had to load down one of my solar panels to drop the voltage down to 13.8 volt.  Being 19 volt OCV i had to load then down with very high load incandescent bank to drop the volage down and start  unscrewing 12 volt incandescent lamps until  12 volt
And put my car battery in circuit and monitor the voltage
  Then I hooked up my inverter and then i had to match my load
 On the inverter and contantly switching things on and off
All day long as more power comes on line I had load it down
To keep voltage in range of 12 and 13 volt.   10 volt is the invter trip out point  and  outputtiing 55  Hz  if it get  low  and  15  volt  is 63 Hz   So  13.8  volt  sweet  spot for  the car battery  and  inverter  at  60  Hz .   So to contant  changing solar  output
Out of 2100 watts if solar got like 850  watts enough to run a electric  space heater on 750 watts.   So at night it was strictly for lighting powering a F40T12 using GE DC 12 volt rapid start lamp and a car stereo to pass time in the dark.  And Though out the night I had get on my exercise bike.  Under heavy load
Sray warm I was making enough power 2 x 300 watt bulbs
 My self putting out about 1 Horse power and being 24 Degrees inside  my own  house  trying  to stay warm .  This  cause  me to  exhaust  my  food supply  much  quicker.  So got my house above  freezing  until  I  cant  stand  it  below  freezing  i can  take  27  F  in  shorts  if  there  no  wind  chill.   So  back on  my  bike  to  run a  car radio  and  two  i ncandescent  ib  a  12 x  12 heating  space  in  my  house.  Talk about Exhausing  week
   Dealing  with  no power .    Playing  electric  grid  operator  at    Home.   My  power  came  back  on Tusday at  noon  and  got  30  mins  of  power for every  2  hours  until  things  slowly  improves until Thursday morming with power rotation ended.
Now dealing  with  broken  pipes  at  Grandpa.    And  I  had  not  had a  shower for  nearly  a  week!

@funkybulb, I also have a solar generator as well with a 800w inverter and USB charger. But I don't have a bigger battery to power up the TV and etc.

I also got impacted with water as well but no busted or broken pipes though. We had no water for almost 5 days. But water comes and goes while still dealing with the winter storm because of a crappy water company we have is Quadvest.

As of right now, we have water, but however we are under a boil water notice until further notice.

Get an inverter type unit, such as the Honda EU2200i.  I lived off them off-grid for years and the power output was indistinguishable from that of the grid.  Other non-inverted generators, however, had noticeably "dirty" waveforms- fluorescent lights would pulsate, ballasts/motors/transformers were noisy, etc.

Get an inverter type unit, such as the Honda EU2200i.  I lived off them off-grid for years and the power output was indistinguishable from that of the grid.  Other non-inverted generators, however, had noticeably "dirty" waveforms- fluorescent lights would pulsate, ballasts/motors/transformers were noisy, etc.

As long as it's a pure sine wave inverter, you'll be ok.

Have a 1.8MW Cat generator at work-motors,lights,transmitters run fine on it.Motors to 20hp 3ph.We just have to watch not overloading it-or its breaker trips off.When on the gnerator run transmitters at low power so as not to OL the generator.Most of the lights here now are LED-work just fine.