When a body having mass m is suspended from the free end of two springs suspended from a rigid s

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When a body having mass m is suspended from the free end of...

When a body having mass $\mathrm{m}$ is suspended from the free end of two springs suspended from a rigid support, as shown in figure, its periodic time of oscillation is $\mathrm{T}$. If only one of the two springs are used, then the periodic time would be ......... (A) $(\mathrm{T} / \sqrt{2})$ (B) $(\mathrm{T} / 2)$ (C) $\sqrt{2} \mathrm{~T}$ (D) $2 \mathrm{~T}$

When a body having mass $\mathrm{m}$ is suspended from the free end of two springs suspended from a rigid support, as shown in figure, its periodic time of oscillation is $\mathrm{T}$. If only one of the two springs are used, then the periodic time would be .........
(A) $(\mathrm{T} / \sqrt{2})$
(B) $(\mathrm{T} / 2)$
(C) $\sqrt{2} \mathrm{~T}$
(D) $2 \mathrm{~T}$

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Key Concepts

Simple Harmonic Motion

Simple harmonic motion is a type of periodic movement where the restoring force acting on a body is directly proportional to the displacement of the body from its equilibrium position. It is characterized by oscillations that follow a sinusoidal pattern, and its dynamics can be completely described by parameters such as mass and the spring constant in the context of a mass-spring system.

Mass-Spring System Oscillation

In a mass-spring system, a mass attached to a spring oscillates about its equilibrium position under the influence of a restoring force provided by the spring. The period of oscillation is determined by both the mass of the object and the stiffness of the spring (quantified by the spring constant), following the relationship T = 2??(m/k).

Effective Spring Constant in Parallel Arrangement

When multiple springs are used in parallel, their individual spring constants add together to yield an effective spring constant that is the sum of the individual constants. This increased stiffness leads to a shorter period of oscillation compared to using a single spring, as the system responds more rapidly to deviations from its equilibrium position.

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