Oscillation, spring constant, damping, displacement help! Auto suspension a) A c

Question

Oscillation, spring constant, damping, displacement help!

Auto suspension a) A car has a mass of 1800 kg.It is supported by four identical springs, one near each wheel. Assume each spring supports ¼ of the weight of the car. Without damping, the vertical oscillation period of the car is 1.2 s. What is the spring constant of each spring? b) Suppose that we add a damping force -bv, where v is the vertical velocity, to each of the four suspension points of the car. What value of b should be chosen so that the vertical oscillation is critically damped? c Suppose that the car described in parts (a) and (b) is riding smoothly along the road, but then at time t-0 encounters a sudden vertical impulse, which imparts a vertical velocity of 0.6 m/s to the car. (In other words, there is an initial condition x( 0)-0, v(1-0)=0.6 m/s, where x is the vertical displacement. ) of the car? Make a plot of this displacement. What is the subsequent vertical displacement x d) What is the maximum displacement of the car after the bump? About how long does it take for the car to return to a displacement less than 1 cm (after passing the maximum)?

Explanation / Answer

here,

a)

mass of car , m = 1800 kg

the mass on each spring , m' = m/4

let the spring constant be K

the oscillation period , T = 2 * pi * sqrt(m'/K)

1.2 = 2 * pi * sqrt(1800/( 4 * K))

solving for K

K = 12324.5 N/m

the spring constant of each spring is 12324.5 N/m

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