3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following second order linear ODE: dx,2 dt n dt2 (0) C dt where is the damping ratio an wn is the natural frequency, both related to k, b, and m (the spring constant, damping coefficient, and mass, respectively) (a) Use the forward difference approximations of (b) Using Δt andd to obtain a finite difference formula for x(t+ 2Δ) (like we did in class for the pendulum angle example). 0.3, solve for 2(0.6) for the case when Ç-0.2, ah-2T, F-0.1, B--2, and С 0.3. Figure 1: Mass spring damper system 3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following second order linear ODE: dx,2 dt n dt2 (0) C dt where is the damping ratio an wn is the natural frequency, both related to k, b, and m (the spring constant, damping coefficient, and mass, respectively) (a) Use the forward difference approximations of (b) Using Δt andd to obtain a finite difference formula for x(t+ 2Δ) (like we did in class for the pendulum angle example). 0.3, solve for 2(0.6) for the case when Ç-0.2, ah-2T, F-0.1, B--2, and С 0.3. Figure 1: Mass spring damper system
Taylor expansion: wx^2 - (w^3 x^4)\/6 + (w^5 x^6)\/120 - (w^7 x^8)\/5040 + (w^9 x^10)\/362880 - (w^11 x^12)\/39916800 + O(x^13).......
0
