1. Given the spring-mass-damper system in the figure below T3 T1 T2 b2 b1 k3 (a) Find the equatio...
Given the data (t1, b) = (-1,-4) (t2, b2) = (0,2) (t3, 63) = (1,2) (t4,64) = (2, -7), find the linear equation f(t) = cit+co that best fits f(ti) = bị. a.(5 points) Find the matrix A for which you can rephrase the problem as solving Ax* 2 2 -7 7 C1 for which x* = [e gives the least-square solution. Со b.(15 points) Solve the least-square problem and find cit+ Co.
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at the right end of the spring k3 and x() is the displacement of mass ml. (Note that the input is displacement, NOT force) k3 k1 m2 (a) (10pts) Draw necessary free-body diagrams, and the governing equations of motion of the system. (b) (10pts) Find the transfer function from the input u() to the output x(t). (c) (10pts) Given the system parameter values of m1-m2-1,...