Answer
given,
mass of the car, m = 1260 Kg
mass on each spring = 1260/4 = 315 Kg
a) frequency, f = 1.6 Hz
spring constant, k = ?
[tex]f = \dfrac{1}{2\pi} \sqrt{\dfrac{k}{m}}[/tex]
squaring both side
[tex]k = 4 \pi^2 f^2 m[/tex]
[tex]k = 4 \pi^2\times 1.6^2\times 315[/tex]
k = 3.18 x 10⁴ N/m
b) frequency of the spring if 4 mass of 70 Kg sit in the car
mass on each spring, [tex]m = \dfrac{1260 + 4\times 70}{4}[/tex]
m = 385 Kg
now,
[tex]f = \dfrac{1}{2\pi} \sqrt{\dfrac{k}{m}}[/tex]
[tex]f = \dfrac{1}{2\pi} \sqrt{\dfrac{3.18\times 10^{4}}{385}}[/tex]
f = 1.45 Hz
hence, frequency of the spring is equal to 1.45 Hz
