Answer:
a) 120341 N/m
b) 1.432 Hz
Explanation:
Given that
Frequency of oscillations of spring, F = 3.27 Hz
Mass of the car, m = 1140 kg
Average mass of passengers, M = 68 kg
The mass on each spring,
m = 1/4 m,
m = 1140 / 4
m = 285 kg
The spring constant on each spring, k is
ω = √(k/m), also,
ω = 2πf, so that
2πf = √(k/m)
If we square both sides, then
4π²f² = k/m
k = 4π²f²m if we substitute, we have
k = 4 * 3.142² * 3.27² * 285
k = 120341 Nm
Since the mass of each person is 68 kg, then the total mass of all passengers would be
68 * 5 = 340 kg
Thus, the total mass of the oscillating system is,
mass of passengers + mass of car
340 kg + 1140 kg
M(total) = 1480 kg
To get the vibrating frequency, we substitute for values in the equation
2πf = √(k/m)
F = 1/2π * √(k/m)
F = 1/2π * √(120341 / 1480)
F = 1/2π * √81.31
F = 0.1591 * 9
F = 1.432 Hz
