A simplified model of a passenger car travelling over a road and vibrating in the vertical

direction is shown below. The mass of the vehicle is $1000$ kg$,$ the spring stiffness of the

suspension system is $500$ kN$/$m$,$ and there is a damping ratio of $=0\mathrm{.}5.$

$($a$)$ Determine the damping coefficient of the suspension system.

$($b$)$ Determine the quality factor, Q$,$ of the system.

$($c$)$ Determine the value for $$when under free oscillation.

$($d$)$ If the road surface is assumed to vary sinusoidally with an amplitude of $0\mathrm{.}025$m over

a length for one cycle of $6$ m$.$ Determine the displacement amplitude of the vehicle if

the vehicle is travelling at $30$ m$/$s$.$

$($e$)$ Use MATLAB to determine the damping constant required to reduce the amplitude of

the vehicle to less than $10$ mm$.$ What other parameters could you change to acheive

the same result?A simplified model of a passenger car travelling over a road and vibrating in the vertical

direction is shown below. The mass of the vehicle is $1000kg,$ the spring stiffness of the

suspension system is $500k\frac{N}{m},$ and there is a damping ratio of $=0\mathrm{.}5.$

$($a$)$ Determine the damping coefficient of the suspension system.

$($b$)$ Determine the quality factor, $Q,$ of the system.

$($c$)$ Determine the value for $$ when under free oscillation.

$($d$)$ If the road surface is assumed to vary sinusoidally with an amplitude of $0\mathrm{.}025m$ over

a length for one cycle of $6m.$ Determine the displacement amplitude of the vehicle if

the vehicle is travelling at $30\frac{m}{s}.$

$($e$)$ Use MATLAB to determine the damping constant required to reduce the amplitude of

the vehicle to less than $10mm.$ What other parameters could you change to acheive

the same result?A simplified model of a passenger car travelling over a road and vibrating in the vertical

direction is shown below. The mass of the vehicle is $1000kg,$ the spring stiffness of the

suspension system is $500k\frac{N}{m},$ and there is a damping ratio of $=0\mathrm{.}5.$

$($a$)$ Determine the damping coefficient of the suspension system.

$($b$)$ Determine the quality factor, $Q,$ of the system.

$($c$)$ Determine the value for $$ when under free oscillation.

$($d$)$ If the road surface is assumed to vary sinusoidally with an amplitude of $0\mathrm{.}025m$ over

a length for one cycle of $6m.$ Determine the displacement amplitude of the vehicle if

the vehicle is travelling at $30\frac{m}{s}.$

$($e$)$ Use MATLAB to determine the damping constant required to reduce the amplitude of

the vehicle to less than $10mm.$ What other parameters could you change to acheive

the same result?