Question 1 (40 points) The system is governed by the dynamic equilibrium equation Eq. (1) S(u)...

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Question 1 (40 points) The system is governed by the dynamic equilibrium equation Eq. (1) S(u) u(t) + 10 u(t) = 0; (0) = 1.0; u(0) = 0.005 Nm Where kg ms-1 [4.103 Nm 1 -0.005 m u 0.005 m S(u)= 4.105Nm-1 u>0.005 m m (1) (A) Draw/sketch the system described by Eq. (1) and indicate (by providing the numbers) the parameters/variables describing the state of the system at time t=0. A schematic (but legible) diagram/sketch indicating the components of the system is sufficient. (10 points) For the system described by Eq. (1), use an explicit integration in time domain (central difference integration method) to calculate the response for u. (B) Determine the time step At you would use for efficient and stable solution. (10 points) (C) Determine (using central difference integration method) the time history (only for the first two time steps: t=At, and t=2^t) of u. Plot the determined time history. (15 points) (D) What would be the time step required for stable solution for u>0.005 m if S(u) is as below S(u)= 4.103 Nm -0.005 m u 0.005 m -6.105Nm-1 ? u > 0.005 m (5 points) Question 1 (40 points) The system is governed by the dynamic equilibrium equation Eq. (1) S(u) u(t) + 10 u(t) = 0; (0) = 1.0; u(0) = 0.005 Nm Where kg ms-1 [4.103 Nm 1 -0.005 m u 0.005 m S(u)= 4.105Nm-1 u>0.005 m m (1) (A) Draw/sketch the system described by Eq. (1) and indicate (by providing the numbers) the parameters/variables describing the state of the system at time t=0. A schematic (but legible) diagram/sketch indicating the components of the system is sufficient. (10 points) For the system described by Eq. (1), use an explicit integration in time domain (central difference integration method) to calculate the response for u. (B) Determine the time step At you would use for efficient and stable solution. (10 points) (C) Determine (using central difference integration method) the time history (only for the first two time steps: t=At, and t=2^t) of u. Plot the determined time history. (15 points) (D) What would be the time step required for stable solution for u>0.005 m if S(u) is as below S(u)= 4.103 Nm -0.005 m u 0.005 m -6.105Nm-1 ? u > 0.005 m (5 points)