Question

Suppose that a car weighing 4000 pounds is supported by four shock absorbers Each shock absorber has a spring constant of 6500 lbs/foot, so the effective spring constant for the system of 4 shock absorbers is 26000 lbs/foot. Assume no damping and determine the period of oscillation of the vertical motion of the car.
Required:
a. Assume no damping and determine the period of oscillation of the vertical motion of the car.
b. After 10 seconds the car body is 1/3 foot above its equilibrium position and at the high point in its cycle. What were the initial conditions?

Answer 1

Answer:

0.43622 seconds

0.9158 foot

-4.43 ffot/sec

Explanation:

we first find the period of oscillation

= 2π√w/gk

= 2π√4000/32x2600

= 2π√0.00481

= 2π0.0694

= 0.43622

b. we find the angular velocity

2π/T

= 2π/0.43622

= 14.41 rad/sec

we find displacement

rom the calculation in the attachment

Ф = -144.1

initial condition

1*cos(-144.1 rad)

= 0.9158 foot

initial velocity of the car

= (-1)(14.41)sin(ω(0)-144.1)

= -4.44 foot/sec