(a) Use MATLAB ODE45 function to solve the below two second order differential equations (MATLAB scripts and calculated results/figures should be copied and pasted to the answer sheet). Plot x

vs. t, i vs. t, and i vs. x,respectively. \ddot{x}+15 \pi x+20 x^{3}=\sin (150 \pi t) ; \quad x_{0}=1 ; \dot{x}_{0}=1 ; \quad t \in[010] 4 \ddot{x}+5 x \cdot \dot{x}+6 x=\sin \left(t^{2}\right) \quad x_{0}=2 ; \dot{x}_{0}=2 ; \quad t \in[0300] (b) Describe the method of using the trajectory graph (velocity vs.displacement) to identify the stability of the system defined by a differential equation. (c) In the motion equation of a MEMS (Micro-electromechanical systems)resonator, identify the factors affecting the natural frequency, and factors that contribute to the system damping. Write down the analytical equation of the fundamental natural frequency. (d) Describe the procedure of fabricating a radio frequency (RF) MEMS switch with the top-down process, sketch out process flow.(6 mark)