1. Circular Motion & Elastic Strings | Finding the extension of a stretched elastic string in uniform circular motion and analyzing forces acting on the system.

2. Vertical Motion & Energy Conservation | Determining the instantaneous rest position of a mass-spring system using energy principles and elastic potential energy.

3. Collisions & Kinetic Energy Loss | Analyzing the oblique impact of two spheres, calculating deflection angles, and determining energy loss due to inelastic collision.

4. Equilibrium & Friction in Mechanics | Computing forces acting on a rod in equilibrium, including tension, friction, and external weights affecting stability.

5. Projectile Motion & Relative Velocity | Deriving trajectory equations, proving velocity relationships, and analyzing simultaneous motion of two projectiles.

6. Simple Harmonic Motion & Resistive Forces | Solving differential equations for velocity under resistive forces, deriving displacement equations, and determining limiting behavior of motion.