In a lot of places you yourself cannot touch it. You can offer the landlord money to fix it, but you should not have to. Fixes probably be simple vibration dampers or could be major work/replacement of furnace.

@crip659 Landlord is not being cooperative unfortunately and not taking any action for this problem. I need to find a practical solution myself.

Is that metal hot? Looks like the exhaust flue for some very nasty gases and carbon monoxide. Given that this is a rental and you have zero experience in home improvement I would hesitate to provide any suggestions whatsoever. You can call an HVAC contractor yourself and just pretend it's your own home and they might make some suggestions. If something gets broken or if the landlord finds out or if someone dies as a result of this then you will have some really big legal issues to deal with.

@MonkeyZeus It is not hot, I can easily touch it. The tube inside, I do not know, maybe hot. I never checked it. The rattling noise comes from that part that looks like a cone and that one is not hot.

You need written authorization from the landlord to fix it plus you need to have it inspected by a licensed inspector after. The only thing you can do yourself right now is have a safety inspector check it, but it making noise might not be enough to flag it for repair. This might come down to a legal matter, moving might make more sense.

I hesitate to provide any suggestions unless that metal can be identified. If you want to skirt around your landlord then call an HVAC contractor since you seem to be willing to spend hundreds of dollars.

@crip659 I see.. Unfortunately I have a contract so I cannot move until next summer. I will have to live with noise it seems..

@MonkeyZeus Yes, ok.. I will try to find an HVAC contractor.. I will maybe just get a possible solution from the contractor and contact my landlord after letting them know and hoping that they pay.. The noise is very annoying especially at night.

If noise is coming from the floor vent/s instead of though the floor, you might be able to block vent and reduce the noise.

I wholeheartedly believe that the noise is annoying; the ticking of a wristwatch in a dresser drawer is enough to keep me up at night. Unfortunately you are in a rental so the only thing you can legally do is continue complaining to the landlord. Sadly I think the "if it ain't broke, don't touch it" mentality is prevalent.

@crip659 It is definitely coming through the floor.

@MonkeyZeus Yes, I will try complaining again.. I know there won't be any outcomes but if it is my only option, that is what I will do..

I couldn't tell from the video but is there enough space on the basement's ceiling to attach acoustic foam? Make sure it's away from heat sources and make sure not to damage any electrical wires, gas pipes, nor water pipes.

@MonkeyZeus It is extremely dirty to attach anything to the ceiling. I would be happier if I could stop that piece from moving so much thus making the rattling noise. It just seems like it needs new screws or some tightening. Or maybe I can somehow attach a weight to it so that it does not rattle..

Where does the pipe go which is visible at the 22-23 second mark? It could help me to identify it's purpose. Also, yes I do believe it is a furnace since you can see a gas supply line at the 16 second mark.

@MonkeyZeus It is going outside like an exhaust. There is also some sort of pump there. But I think (again I have zero experience) that is the inner tube that is carrying the steam, but the rattling noise is coming from the bigger cone shaped piece that I put my stick on, it is more like a cover to the inner pipe (I think), hence it is not warm.

A non-destructive solution could be to buy two medium Dewalt trigger clamps and attach them to the bottom of the round rattling thing. Once you do that then you can hang some weights on the end of the clamp's bar until the noise goes away. Just be careful not to break anything.

Dewalt is not the only brand that makes trigger clamps. You can find plenty of other brands but I personally own Dewalt clamps and they have lived through a considerable amount of abuse.

@MonkeyZeus Thank you, I will try this. I was trying to find a way to attach some weights, trigger clamps can work. Maybe I can put the weight in between and attach these instead of hanging the weights? Like making the weight a sandwich between clamps and the rattling part? Would you have weight suggestions too that I can try?

If the clamp's bar can fit through the hole on a standard weight plate then you can try adding 5 pound weights (or smaller) until the noise stops.

You might discover that simply clamping a bar or two eliminates the noise and no further action is needed. If you do end up using weights then just be careful that it doesn't warp the metal over time. And of course be sure to remove it if the landlord does any inspections or repairs while you're not home.

@MonkeyZeus Thank you very much, I also thought maybe the clamping bars will already solve it with their own weight (hopefully). I will try this as soon as possible. Thank you for your time and your advise.

No problem, let me know how it turns out an I can turn my comments into an answer =)

@MonkeyZeus Sure, will do. But since it is summer time now, the furnace does not kick on very often. Yesterday it did since it was a bit cold. I think I will try 4 of these: amazon.ca/gp/product/B00004TRCD

Do you have access to the thermostat? Set the temperature high enough to force the furnace to kick on. I find it strange that you wish to implement a solution which won't be tested until 5 months from today.

As for those clamps, you might have interference/clearance issues if you try to attach weights.

@MonkeyZeus I will try setting the thermostat up but if the really hot weather (~30 degrees) comes before I can get these, I might not be able to start the furnace. I am not planning on attaching weights to those clamps, but rather attaching 4 of them to add 1 kilo in total to the rattling piece. (Each is around 250 gr according to the product page)

Boy you weren't kidding when you said "I have zero experience in home improvement / maintenance." You can hold a bowl of ice next to the thermostat for a few minutes. If you're feeling adventurous then you can remove the thermostat's face plate and cross two specific wires to activate the furnace.

I know where the device is where you set the target temperature (it is in the building hallway) but I do not know where the actual sensor is that reads the temperature. And playing with the wires I definitely do not want to. I think you can still provide your idea as an answer and get upvotes already and I can mark it as accepted once I test it. If you see my Stackoverflow profile I do not leave my questions unaccepted and I mostly upvote any answer for the effort and the time person committed (unless it is just plain wrong). @MonkeyZeus

use an expandable shower/curtain rod to push on it all the time the same as you did with your hand.

@dandavis Very good idea, I will check if there are any colons, walls I can use.

GET A CO DETECTOR. You've got plenty of advice on the noise. That furnace is filthy, it is obviously not being maintained at all and your bedroom is directly above it. You hopefully have no issue but it's always a good idea to have a CO detector in your bedroom, a better idea in a rental where you have no control of maintenance, and even more when maintenance is obviously not occurring. It's $20, just get one and leave it anywhere in your bedroom.

Question: Where are you? Are you actually using heat now or is this also an air conditioner? Are you using the A/C now? If so I have another idea.

@jay613 I am located in Ontario / Canada. This is not an air conditioner, we do not have an air conditioner. We have radiators in the apartment. Heating is not on these days since weather is warm, it only turned on at nights a few days ago.