Because the stiffness of the outer support beam along the y-axis (KyoKy) is very large, only the inner-frame is driven to vibrate along the y-axis by the Coriolis force, which induces the alternating capacitance between the inner-frame and fixed sense electrode. We can obtain the rotation rate along the z-axis by detecting the alternating capacitance.Figure 1.(A) The frame of the SMG. (B) The simple model of SMG. (C) The picture of the processed SMG.The simplified motion equations of SMG are described by:mxx��+Rxx�B+Kxx=Fe+n(1)myy��+Ryy�B+Kyy=?2my��x�B(2)where x and y are separately the drive axis displacements and sense axis displacements in meters, �� the rotation rate along the z-axis in radians/second, mx (mx=m1+m2) and my (my=m2) the drive proof mass and the sense proof mass in kilograms, Rx and Ry the damping in Newtons/meter/second, Kx and Ky the stiffness in Newtons/meter, and ?2m x�� the denote of the Coriolis force.

Fe (Fe=Fdsin��dt) is the electrostatic force used to maintain the drive-mode vibration at a specified amplitude in terms of displacement, and at a resonant frequency of the drive-mode. Mechanical thermal noise on the drive axis is represented by the random force n(t), in units of force.Ignoring the influence of the random force n(t), the drive axis displacements and sense axis displacements in the steady state are described by:x��Axsin(��dt+��)(3)y��Aysin(��dt+��+��)(4)where Ax=Fdmx(��nx2?��d2)2+��nx2��d2Qx2; ��=?tg?1(��nx��dQx(��nx2?��d2)); Ay��?2����dAx(��ny2?��d2)2+��ny2��d2Qy2; ��=tg?1(Qy(��ny2?��d2)��d��ny); ��nx =(Kx/mx)(1/2); ��ny =(Ky/my)(1/2); Qx=mx��nx/Rx, Qy=my��ny/Ry.

When ��d=��nx=��ny, the maximum drive axis displacements and sense axis displacements are described by:x(t)=FdQxKxsin(��dt?��2)(5)y(t)=?2FdQxQy��Kx��dsin(��dt?��2)(6)3.?Mechanical Thermal NoiseConsider the damped harmonic oscillator:mxx��+Rxx�B+Kxx=n(7)The presence of damping in the system suggests that any oscillation would continue to decrease in amplitude forever. Inclusion of the fluctuating force n(t) prevents the system temperature from dropping below that of the system’s surroundings. The damper provides a path for energy Drug_discovery to leave the mass-spring system. This is the essence of the Fluctuation-Dissipation Theorem. According to Equipartition, if any collection of energy storage mode is in thermal equilibrium, then each mode will have an average energy equal to (1/2)kBT where kB is Boltzmann’s constant(1.38��10-23J/K) and T is the absolute temperature in degrees Kelvin. A mode of energy storage is one in which the energy is proportional to the square of some coordinate; e.g., kinetic and spring potential.