The secondary unbalanced forces of reciprocating masses in the engine is

Explanation:

The unbalanced force due to reciprocating masses varies in magnitude but is constant in direction while due to the revolving masses, the unbalanced force is constant in magnitude but varies in direction.

Unbalanced force:

\({F_U}= m{ω ^2}R\left( {\cosθ + \frac{{\cos2θ }}{n}} \right) \)

\(F_U= m{ω ^2}R\cosθ + m{ω ^2}R \times \frac{{\cos2θ }}{n}\)

\(F_P=m{ω ^2}R\cosθ\) = Primary unbalance force.

\(F_S=m{ω ^2}R \times \frac{{\cos2θ }}{n}\) = Secondary unbalance force.

where n = ratio of the length of connecting rod to crank radius.

Thus from the expression of secondary force, \(F_S=m{ω ^2}R \times \frac{{\cos2θ }}{n}\), we can see that Fs is inversely proportional to n (ratio of the length of connecting rod to crank radius).