A cone model is tested on a setup with free oscillations in a supersonic wind tunnel at Mach numbers M= 1.75, 2.0, 2.25, 2.5, 3.0, and 4.0. It is demonstrated that the model is dynamically stable at M= 2.5, 3.0, and 4.0. Self-induced oscillations with soft excitation are observed at M= 1.75 and 2.0; self-induced oscillations with hard excitation are detected at M= 2.25. It is found that the amplitude of these oscillations at M= 1.75 depends on the initial disturbance, Reynolds number, and dimensionless moment of inertia of the model. In the case of soft excitation, the amplitude of oscillations grows slowly at the beginning, and then a jump occurs, which is most clearly expressed at M= 2.0.
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