Answer
60.75 kg
Work Step by Step
Here each spring supports one-quarter of the total mass M. Let's apply equation 10.11 $\omega=\sqrt {\frac{k}{m}}$ for one spring.
$\omega=\sqrt {\frac{k}{m}}=> m=\frac{k}{\omega^{2}}-(1)$
We know that, $T=\frac{2\pi}{\omega}-(2)$
(2)=>(1),
$m=\frac{kT^{2}}{4\pi^{2}}$ ; Let's plug known values into this equation.
$\frac{M}{4}=\frac{1.3\times10^{5}N/m(0.37\space s)^{2}}{4\pi^{2}}=>M=1803\space kg$
M=mass of empty car + mass of 4 passenger
Mass of 4 passenger = 1803 kg - 1560 kg = 243 kg
So, the mass of one passenger = $243\space kg \div 4=60.75\space kg$
