Front wheel wobble at high speeds

You're likely experiencing speed wobble/death wobble:

Wobble, shimmy, tank-slapper, speed wobble, and even death wobble are all words and phrases used to describe a quick (4–10 Hz) oscillation of primarily just the steerable wheel(s) of a vehicle. Initially, the rest of the vehicle remains mostly unaffected, until translated into a vehicle yaw oscillation of increasing amplitude producing loss of control. Vehicles that can experience this oscillation include motorcycles and bicycles, skateboards...

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In two-wheeled vehicles

Wobble or shimmy begins when some otherwise minor irregularity accelerates the wheel to one side. The irregularity may be a wheel which is out-of-round, out-of-true, or out-of-balance. As the wheel rotates, it will exert a cyclic load to the vehicle frame, which if matched with the system's (vehicle and attached accessories) resonant frequency, can produce a speed wobble. During the wheel rotation, a restoring force is applied in phase with the progress of the irregularity, and the wheel turns to the other side where the process is repeated. If there is insufficient damping in the steering the oscillation will increase until system failure. The oscillation frequency can be changed by changing the forward speed, making the bike stiffer or lighter, or increasing the stiffness of the steering, of which the rider is a main component. While wobble or shimmy can be easily remedied by adjusting speed, position, or grip on the handlebar, it can be fatal if left uncontrolled.

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An academic paper that investigated wobble through physical experimentation and computer modeling concludes: "the influence on wobble mode of front tire characteristics, front frame inertia and chassis stiffness were shown. In particular, it shows that [by] increasing front tire inflation, chassis stiffness, and front frame inertia about steering axis and decreasing sideslip stiffness of front tire, wobble mode damping is improved, promoting vehicle stability."

So this can (and does...) happen with just about any bicycle. And as the term "death wobble" implies, it can be really dangerous.

When it happens, do not panic. You need to change the resonant frequency to get the oscillations to stop. One of the worst things you can do is grab your handlebars tighter and try to outmuscle the oscillations - grabbing the bars tightly isn't going to "increase the stiffness of the steering" because your upper body is up in the air, attached to the bars by two flexible arms. So you're really not adding any stiffness to the steering if you grab grab your bars harder. Not only that, if gripping the bar tighter doesn't work (and it probably won't...), more powerful oscillations will be transmitted through your tighter grip to you and your mass will be quickly added to the oscillations and you'll almost certainly crash.

Relax your grip on your handlebars, and to really change the resonant frequency of your bicycle, clamp your knees against the top bar.

The relatively low pressure of a 37 tire might be a contributing factor.