Question

Two identical springs of spring constant $k$ are To block of mass $m$ and to fixed supports attached to a block in the figure. The time period of oscillation as hown is $\pi$ (a) $2 \pi \sqrt{\frac{m}{k}}$ (b) $2 \pi \sqrt{\frac{m}{2 k}}$ (c) $2 \pi \sqrt{\frac{2 m}{k}}$ (d) $\pi \sqrt{\frac{m}{2 k}}$

Name: Problem 72, Chapter 14: Objective NCERT at your FINGERTIPS: Physics
Uploaded: 2021-09-28T10:36:35-08:00
Duration: 3 min 30 s
Channel: Mahendra Kumar
Description: Two identical springs of spring constant k are To block of mass m and to fixed supports attached to a block in the figure. The time period of oscillation as hown is π(a) 2 π√((m)/(k)) (b) 2 π√((m)/(2 k)) (c) 2 π√((2 m)/(k)) (d) π√((m)/(2 k))

   Two identical springs of spring constant $k$ are
To block of mass $m$ and to fixed supports attached to a block in the figure. The time period of oscillation as hown
is
$\pi$
(a) $2 \pi \sqrt{\frac{m}{k}}$
(b) $2 \pi \sqrt{\frac{m}{2 k}}$
(c) $2 \pi \sqrt{\frac{2 m}{k}}$
(d) $\pi \sqrt{\frac{m}{2 k}}$

Objective NCERT at your FINGERTIPS: Physics

NCERT 11th Edition

Chapter 14, Problem 72

Instant Answer

Solved by Expert Mahendra Kumar

09/28/2021

Step 1

The spring constant of each spring is $k$. Show more…

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Two identical springs of spring constant $k$ are To block of mass $m$ and to fixed supports attached to a block in the figure. The time period of oscillation as hown is $\pi$ (a) $2 \pi \sqrt{\frac{m}{k}}$ (b) $2 \pi \sqrt{\frac{m}{2 k}}$ (c) $2 \pi \sqrt{\frac{2 m}{k}}$ (d) $\pi \sqrt{\frac{m}{2 k}}$

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Key Concepts

Simple Harmonic Motion

This concept describes the oscillatory motion where the restoring force is proportional to the displacement from equilibrium, resulting in a sinusoidal oscillation with a constant period. It forms the basis for analyzing systems like mass-spring oscillators.

Effective Spring Constant

When multiple springs are used together, their overall stiffness is determined by how they are arranged. For springs in parallel, the effective spring constant is the sum of the individual spring constants, which increases the system's restoring force and affects the oscillation period.

Oscillation Period

The time period of a mass-spring system undergoing simple harmonic motion is given by the formula T = 2??(m/k_eff). This relationship shows how the mass and the effective spring constant of the system determine the duration of one complete oscillation cycle.

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