A flywheel is attached to an engine that has a sinusoid Torque amplitude of $250N*m.$ The

car has differential drive gear ratio of $2$:$1$ to and gear ratios for gears first through sixth of

$3$:$1,2\mathrm{.}07$:$1,1\mathrm{.}43$:$1,1$:$1,0\mathrm{.}84$:$1,$ and $0\mathrm{.}56$:$1$ respectively. $($The total gear ratio G is the product

of the differential gear ratio and the gear ratio of the current gear you are in$).$ The moment

of inertia of the rotational components of the car $($excluding the flywheel$)$ is approximated

by $J=J_0(1+0\mathrm{.}04+0\mathrm{.}0025G^2)kg*m^2,$ where $J_0=49kg*m^2.$ Approximate frictional

damping in the car $($including engine, transmission$)$ is $B=7\frac{N*m}{ra\frac{d}{s}}.$

a$.$ Assume the vehicle has no flywheel and is cruising in first gear at $2000$ rpm $($living wild$).$

Determine the fluctuation in angular velocity of the wheels. ANS: $=0\mathrm{.}0215$

b$.$ Determine the fluctuation in angular velocity of the wheels if in sixth gear at $2000$ rpm $.$

c$.$ Determine the mass moment of inertia of flywheel required to reduce angular velocity

fluctuation in half when the vehicle moves in sixth gear.

d$.$ Choose the mass and dimensions of the steel flywheels to obtain the desired MOI.

$($assume the material is steel with density of $8000k\frac{g}{m^3}$ and a thickness of $5$ cm $)$