The periodic time of a simple pendulum is T1. Now if the point of suspension of this pendulum st

Step 1: Given that the point of suspension of the pendulum is moving along the vertical directio

The periodic time of a simple pendulum is T1. Now if the...

The periodic time of a simple pendulum is $\mathrm{T}_{1}$. Now if the point of suspension of this pendulum starts moving along the vertical direction according to the equation $\mathrm{y}=\mathrm{kt}^{2}$, the periodic time of the pendulum becomes $\mathrm{T}_{2}$ Therefore, $\left(\mathrm{T}_{1}^{2} / \mathrm{T}_{2}^{2}\right)=\ldots \ldots \ldots .\left(\mathrm{k}=1 \mathrm{~m} / \mathrm{s}^{2} \& \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$ (A) $6 / 5$ (B) $5 / 6$ (C) $4 / 5$ (D) 1

Key Concepts

Simple Pendulum

This concept involves a mass (or bob) suspended from a fixed pivot by a lightweight string or rod, which swings under the influence of gravitational force. For small angular displacements, the motion approximates simple harmonic motion, and its period is given by T = 2??(l/g), where l is the length of the pendulum and g is the acceleration due to gravity.

Effective Gravitational Acceleration

When the base or point of suspension of a pendulum is itself accelerating, the pendulum experiences a modified gravitational field. The effective gravitational acceleration is the sum of the actual gravitational acceleration and any additional acceleration from the moving reference frame, thereby influencing the dynamics of the pendulum’s swing.

Accelerated Frames and Inertial Forces

In non-inertial (accelerated) frames, fictitious or inertial forces must be considered to explain the observed motion. These forces arise because the reference frame is accelerating relative to an inertial frame, causing apparent modifications in forces such as gravity that affect the motion of objects like the pendulum.

Period Adjustment Due to Acceleration

This concept covers how the period of oscillation for systems like the simple pendulum is altered by changes in the effective gravitational acceleration. If the support of the pendulum accelerates (for instance, upwards), the additional acceleration alters the net gravitational force acting on the bob, leading to a change in the period compared to when the pendulum is suspended from a fixed pivot.

Please give Ace some feedback