Mechanical Engine Give step by step solutic The uniform rod AB of mass 10 kg can rotate about an axis at A and is connected to a triang wooden block of mass 50 kg and height h, 0.15 m to form a composite pendulum as show in

Mechanical Vibrations

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1.19. A spherical ball of weight w and radius r rolls back and forth without slipping in a plane motion inside a bowl whose surface is a surface of revolution formed by the sinusoidal curve v=r(1-0 Find the Rayleigh's method its period for small oscillations. 1.30 COS TX 4r

11 A cylinder of mass m and mass moment of inertia J is free to roll without slipping, but is restrained by the spring k, as shown in Fig. P2-11. Determine the natural frequency of oscillation. Use:force balance method m. Jo k

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question 2 A mass ! hangs on the end of a cord around a pulley of radius 5 and moment of inertia 6, rotating with an angular velocity ,, as shown in the figure below. The rim of the pulley is attached to a spring (with constant 7). Assume small oscillations so that the spring remains essentially horizontal and neglect friction so that the conservation of energy of the system yields: 1 2 !91 + 1 2 6,1 + 1 2 7;1 − !); = =, ?ℎABA , = 9 5 , = = CDE&/, ; = FG&H'5CA!AE/ IBD! AJ(G'GKBG(! Find the natural circular frequency of the system in terms of !, 5, 7,6, and ).

A mass of 0.75kg is attached to one end of a horizontal spring, of spring constant 400Nm-1. The other end of the spring is attached to a regid wall. The mass is pushed so that at time t=0 it is 4.0cm closer to the wall than the equilibrium position and is traveling towards the wall with a velocity of 0.50ms-1. a) determine the total energy of the oscillating system. b) obtain an expression for the displacement of the mass in the form x=Acid(wt+π)m, giving numerical values for A, w and phi

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