A spring hangs from the ceiling with an unstretched length of TI! xo = 0.49 m. A mị = 8.3 kg block is hung from the spring, causing the spring to stretch to a length xị = 0.80 m. Find the length x2 of the spring when a m2 = 1.7 kg block is hung from the spring. For both cases, all vibrations of the spring are allowed to settle down before any measurements are made. X2 = m,

ma=12kg and L=1.5m

1.9.3 u(t) due to the road surface. All displacements are measured from equilibrium positions. y(1) A M Body mass Spring K B Shock absorber Axle and wheel mass u(1) A Road profile Figure 1.6 Quarter-car Suspension model of Exercise 54. eeeee M₁ 00000 54 The mass-spring-damper system of Figure 1.6 models the suspension system of a quarter-car. Obtain a state-space model in which the output represents the body mass vertical movement y and the input represents the tyre vertical movement

A 1.4 kg mass attached to a horizontal spring oscillates at a frequency of 2.1 Hz. At t =0 s, the mass is at x= 1.1 m and has vx =− 2.9 m/s. What is the position (in meters) at t =2 s?