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On A Rotating Frame 15. Problem 1.15: A Mass M Moves Within A Slot Of Length L Located Along A Diame

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on a rotating frame 15. Problem 1.15: A mass m moves within a slot of length L located along a diameter of a horizontal rotating platform. It is further restrained by spring k and dashpot c, as shown in Fig. P1.15. The spring is unstretched when the mass is located at the center of the slot. The platform rotates at a constant angular velocity 2. Derive the equation(s) of motion for the system. litt 212 Figure P1.15 Mass-spring-dashpot system inside diametrical slot in a rotating platform
(40 pts) For the system shown in Figure P1.15 (Problem 1.15). (a) (7 pts) Formulate the equation of motion when the spring is nonlinear. That is, consider the spring constant given by k = ko 1+ or the spring force given by f = ko 1+0 x. Alternatively, this force is a conservative force with potential energy given by v = k ) (6) (5 pts) Convert the equation of motion into two first-order ordinary differential equations. (c) (7 pts) Print out the Matlab program(s) for numerical solution of the equations using ode45 Use these fixed constants in the program: m = 1kg, C = 18 N/), do - 0.5 m, ko 1000 N/m, and n = 10 rad/s. Use the same initial conditions: X(t = 0) - 0,0 0 0.01. (d) (5 pts) Obtain the plot of the solution X(t) vs. for in the interval of 0 and 4.5 s. (e) (6 pts) Obtain displacements X(t) at the steady-state (you may need to extend the integration time) for values of given in the table below. Steady-state Displacement (m) (rad/s) 20 30 31 32 sign for the (1) (10 pts) Repeat the above calculation when the + sign in part(a) is changed to nonlinear term Steady-state Displacement (m) (rad/s) 20 30 31 . 33 34