二、计算题(共3题,50分) 1, A cart-pendulum system is shown below. The cart and the pendulum have the same mass of m and connected

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二、计算题(共3题,50分) 1, A cart-pendulum system is shown below. The cart and the pendulum have the same mass of m and connected by a massless rigid bar of length I. Two springs are of same stiffness k and k = mg/l. (a) Establish the equation motion of the system using two generalized coordinates . (For the study of small vibration, substitute sin 80 and 1 into the obtained EOM.); cos (b) Find its natural frequencies, modal vectors and modal matrix; (c) The cart is at rest. If the cart is hit by an impulse I, find the response of the system. Tain an 3. " -0000000 ooooooo IQH 2₂ A thin uniform rectangular section steel beam (length 1, density p, cross section area 4, bending stiffness EI) is clamped at one end and the other end is a mass lump of m as shown below. (a) Find the characteristic equation in terms of system parameters. (b) Determine the first natural frequency with Raleigh's method. A suggested deflection shape function is w (x)=(x/L). F EI, 1, p.A m