A block of mass m = 5 Kg is attached to a spring of spring constant k. The block oscillates in simple harmonic motion on a frictionless horizontal surface. The block-spring total mechanical energy is 14.4 J. The maximum velocity of block, vmax,

Fig. P4.6 4.22. Derive the differential equation of motion of the simple vehicle model shown in Fig. P4.7. The vehicle is assumed to travel over the rough surface with a constant vehicle speed v. Obtain also the steady state response of the vehicle. For this system, let m = 10kg, k = 4 x 103 N/m, c = 150N · s/m, i = 2 m, and the amplitude Yo = 0.1 m. Determine the maximum vertical displacement of the mass and the corresponding vehicle speed. Determine also the maximum dynamic force transmitted to the mass at the resonant speed. m 2πη y = Y, sin y Fig. P4.7

A vibratory system consists of a spring of stiffness 5 N/mm and a mass of 10 kg. Mass of spring is 3 kg. The natural frequency of the system in rad/sec is

A mass is suspended from a spring and is pulled down 3 cm from equilibrium and released. It completes a period in 2 seconds. Ignoring damping factors, find the function for the displacement from equilibrium h(t) in centimeters t seconds after the mass is released.