As shown in figure (a) and (b), a body of mass m is attached at the ends of the spring system. A

step 1 Hello and welcome to this video solution of numerate. So we are given two spring mass systems. S

As shown in figure (a) and (b), a body of mass m is attached...

As shown in figure (a) and (b), a body of mass $\mathrm{m}$ is attached at the ends of the spring system. All springs have the same spring constant $\mathrm{k}$. Now when both systems oscillate along vertical direction, the ratio of their periodic time is ....... (A) $1 / 4$ (B) $1 / 2$ (C) 2 (D) 4

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Key Concepts

Simple Harmonic Motion

Simple harmonic motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the negative of the displacement. This kind of motion is characterized by sinusoidal oscillations with a specific period and frequency, which remain constant for small amplitudes.

Mass-Spring System

The mass-spring system is a classic example in the study of SHM, where a mass attached to one or more springs oscillates under the influence of the restoring force provided by the springs. The behavior of the system is dictated by the mass and the spring constant, leading to predictable oscillatory motion.

Equivalent Spring Constant

When multiple springs are connected in series or parallel, they can be replaced by an 'equivalent spring constant' that simplifies the analysis of the system. This equivalent constant depends on the configuration of the springs and directly influences the period and frequency of the oscillations.

Period of Oscillation

The period of oscillation in a mass-spring system is the time it takes for the system to complete one full cycle of motion. It is determined by the mass and the effective spring constant of the system, typically expressed by the relation T = 2??(m/k_eff), meaning that alterations in either the mass or the stiffness of the springs will affect the oscillation period.

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