Theory of Machine
The natural frequency of free transverse vibrations due to uniformly distributed load acting over a simply supported shaft is (where δS = Static deflection of simply supported shaft due to uniformly distributed load)

0.5615/ √δS
0.571/ √δS
0.4985/ √δS
0.6253/ √δS

ANSWER DOWNLOAD EXAMIANS APP

Theory of Machine
The velocity of piston in a reciprocating steam engine is given by (where ω = Angular velocity of crank, r = Radius of crank pin circle, θ = Angle turned by crank from inner dead center, and n = Ratio of length of connecting rod to the radius of crank)

ωr [sin θ + (sin 2θ/n)]
ωr [cos θ + (cos 2θ/n)]
ω²r [cos θ + (cos 2θ/n)]
ω²r [sin θ + (sin 2θ/n)]

ANSWER DOWNLOAD EXAMIANS APP