Mechanical engineeringA machine weighs $20kg$ and is supported on springs and dashpots. The total stiffness of the springs

is $15\frac{N}{m}m$ and the damping constant is $0\mathrm{.}5\frac{N}{m}\frac{m}{s}.$ The system is initially at rest and a velocity of

$100m\frac{m}{s}$ is imparted on the mass. Determine the velocity after $0\mathrm{.}5s.$

$(5$ marks$)$