Question

My pickup truck as a weight of 4500 lbs and a bed capacity of 1000 lbs. When I drive along a bumpy road with an empty truck, the truck oscillates with a frequency f = 4 cycles/sec.

1. a) What is the spring constant of the suspension?

2. b) If I add 1000 lbs in the bed of the truck, at what frequency will the truck oscillate?

Answer 1

a)
Frequency of oscillation, f = 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