Question

There is a car, weighing 4500 lbs with a bed capacity of 1000 lbs. When driving on an empty road, the truck oscillates with a frequency f = 4 cycles/sec. a

) What is the spring constant of the suspension?

b) If 1000 lbs are added to the bed of the truck, at what frequency will the truck oscillate?

Answer 1

a)
Frequency of oscillation, f = 4 cycles/sec
= 4 Hz
Angular velocity, = 2 * f
= 2 * 4
= 25.13 rad/s

Spring constant, k = m * ²
Where m is the mass of the truck,
m = 4500 lbs = 2041.166 kg
k = 2041.166 * (25.13)²
= 1.29 * 10⁶ N/m

b)
k is independent of the mass and it remains the same.
= SQRT[k/M]
Where M = 5500 lbs = 2494.758 kg
= SQRT[(1.29 * 10⁶) / 2494.758]
= 22.73 rad/s

f = / 2
= 22.7 / (2)
= 3.6 Hz = 3.6 cycles/sec