x = 4.2cos10πt + 2.6sin10πt
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Your post is very unclear. Could you clarify what you mean by " the rotary disk"? What does a disc mean in this context?
angular velocity = angle / time ; full rotation = 360° = 2 pi ; in 0.04 sec => omega = 360° / 0.04s = 90° / 0.01s = 9000° / s or 2 pi / 0.04s = 50 pi / s in radians. But it's not clear how the equation for x should come into play. It clearly has a period of 1/5 sec (10 pi (1/5) = 2 pi) or maybe half of that, by no means 0.04 sec.