Balancing of reciprocating masses — to achieve dynamic balance in a multi-cylinder engine or mechanism, which components must be balanced?

Introduction / Context: Reciprocating engines produce unbalanced primary (once-per-rev) and secondary (twice-per-rev) inertia forces and corresponding couples that cause vibration. Effective balancing aims to reduce both categories to acceptable levels for smooth operation.

Given Data / Assumptions:

• Multiple cylinders or counterweights can be arranged.
• Connecting rod obliquity introduces secondary components.
• Dynamic balance demands control of forces and resulting couples.

Concept / Approach: Primary components arise from piston acceleration proportional to ω²r; secondary components arise from higher harmonic terms (∝ ω²r·l⁻¹ effects). Proper phasing and magnitudes of masses across cylinders (or added balance shafts) can cancel both forces and couples.

Step-by-Step Solution:

Verification / Alternative Check: Many inline-4 engines balance primary forces but require twin balance shafts to mitigate secondary forces.

Why Other Options Are Wrong:
Primary only — Leaves secondary vibration.
Secondary only — Leaves primary shake.
none of these — Incorrect because both sets matter.

Common Pitfalls: Assuming force balance alone suffices; unbalanced couples can still cause rocking.

Final Answer: both (a) and (b).