A simple pendulum is executing S.H.M. around point O between the end points B and C with a perio

step 1 Hello and welcome to this video solution of numerate. So here we are having a simple pendulum th

A simple pendulum is executing S.H.M. around point O between...

A simple pendulum is executing S.H.M. around point $\mathrm{O}$ between the end points $B$ and $C$ with a periodic time of $6 \mathrm{~s}$. If the distance between $\mathrm{B}$ and $\mathrm{C}$ is $20 \mathrm{~cm}$ then in what time will the bob move from $C$ to $D$ ? Point $D$ is at the mid-point of $C$ and $\mathrm{O}$. (A) $1 \mathrm{~s}$ (B) $2 \mathrm{~s}$ (C) $3 \mathrm{~s}$ (D) $4 \mathrm{~s}$

A simple pendulum is executing S.H.M. around point $\mathrm{O}$ between the end points $B$ and $C$ with a periodic time of $6 \mathrm{~s}$. If the distance between $\mathrm{B}$ and $\mathrm{C}$ is $20 \mathrm{~cm}$ then in what time will the bob move from $C$ to $D$ ? Point $D$ is at the mid-point of $C$ and $\mathrm{O}$.
(A) $1 \mathrm{~s}$
(B) $2 \mathrm{~s}$
(C) $3 \mathrm{~s}$
(D) $4 \mathrm{~s}$

Key Concepts

Displacement-Time Relation in SHM

In SHM, the displacement of the system as a function of time is described by sinusoidal functions (usually sine or cosine). This relationship allows us to determine the time taken to move between specific positions by solving for the phase (or time) corresponding to a given displacement, using the inverse trigonometric functions.

Angular Frequency

Angular frequency is a measure of how rapidly the system oscillates in radians per unit time and is calculated as 2? divided by the period. It plays a key role in the mathematical description of SHM, connecting the time period with the phase of the oscillation according to trigonometric functions.

Time Period

The time period is the duration required to complete one full cycle of oscillation. In the context of SHM, it is a crucial quantity as it links the dynamics of the system to its frequency and angular frequency. It defines the overall timing characteristics of the motion regardless of the varying speeds through different phases of the oscillation.

Simple Harmonic Motion

Simple harmonic motion (SHM) is a type of oscillatory motion where the restoring force is directly proportional to the displacement and acts in the opposite direction. This concept is fundamental in understanding how pendulums, springs, and many other physical systems behave, especially under small oscillations.

Please give Ace some feedback