When two blocks A and B coupled by a spring on a...

When two blocks $A$ and $B$ coupled by a spring on a frictionless table are stretched and then released, then (a) kinetic energy of body at any instant after releasing is inversely proportional to their masses (b) kinetic energy of body at any instant may or may not be inversely proportional to their masses (c) $\frac{\mathrm{KE} \text { of } B}{\mathrm{KE} \text { of } A}=\frac{\text { mass } \text { of } \mathrm{B}}{\text { mass of } A}$, when spring is massless (d) both (b) and (c) are correct

When two blocks $A$ and $B$ coupled by a spring on a frictionless table are stretched and then released, then
(a) kinetic energy of body at any instant after releasing is inversely proportional to their masses
(b) kinetic energy of body at any instant may or may not be inversely proportional to their masses
(c) $\frac{\mathrm{KE} \text { of } B}{\mathrm{KE} \text { of } A}=\frac{\text { mass } \text { of } \mathrm{B}}{\text { mass of } A}$, when spring is massless
(d) both (b) and (c) are correct

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Key Concepts

Conservation of Energy

In any isolated system, especially one without friction, the principle of conservation of energy dictates that the total energy (sum of potential and kinetic energies) remains constant over time. This concept is fundamental in analyzing the evolution of mechanical systems, including those that involve oscillations or interactions between coupled objects.

Normal Modes in Coupled Oscillators

When two or more objects are connected (for example, by a spring), the system can oscillate in specific patterns called normal modes. Each mode represents a unique way in which the system can move where all parts oscillate at a common frequency. Analyzing these modes simplifies the understanding of complex dynamics by decoupling the motion into independent oscillatory components.

Mass-Dependent Kinetic Energy Distribution

In systems with coupled masses, the way kinetic energy is shared between the masses depends on their individual properties and the dynamics of how energy is transferred through the coupling element. This concept highlights that kinetic energy distributions are influenced by the masses and the mode of oscillation, meaning that the relationship between mass and kinetic energy can vary according to the specific conditions of the system.

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