For the following questions, statement as well as the...

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. (a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$. (b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1$ (c) Statement $-1$ is true, statement $-2$ is false (d) Statement $-1$ is false, statement $-2$ is true (A) a (B) $b$ (C) $\mathrm{c}$ (D) d Statement $-1:$ For a particle executing S.H.M. with an amplitude of $0.01 \mathrm{~m}$ and frequency $30 \mathrm{hz}$, the maximum acceleration is $36 \pi^{2} \mathrm{~m} / \mathrm{s}^{2}$. Statement $-2:$ The maximum acceleration for the above particle is $\pm \omega 2 \mathrm{~A}$, where $\mathrm{A}$ is amplitude. (A) a (B) $\mathrm{b}$ (C) $c$ (D) $\mathrm{d}$

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement
$-2$ is not the correct explanation of statement $-1$
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
(A) a
(B) $b$
(C) $\mathrm{c}$
(D) d
Statement $-1:$ For a particle executing S.H.M. with an amplitude of $0.01 \mathrm{~m}$ and frequency $30 \mathrm{hz}$, the maximum acceleration is $36 \pi^{2} \mathrm{~m} / \mathrm{s}^{2}$.
Statement $-2:$ The maximum acceleration for the above particle is $\pm \omega 2 \mathrm{~A}$, where $\mathrm{A}$ is amplitude.
(A) a
(B) $\mathrm{b}$
(C) $c$
(D) $\mathrm{d}$

Key Concepts

Amplitude

The amplitude in SHM refers to the maximum displacement from the equilibrium position. It determines the extent of the oscillation and, when combined with other parameters like angular frequency, helps quantify other dynamic properties such as maximum velocity and acceleration.

Maximum Acceleration in SHM

The maximum acceleration in SHM is derived from the kinematics of the oscillatory motion and is given by the formula a_max = ?²A, where ? is the angular frequency and A is the amplitude. This relationship is key for evaluating the extremal dynamic forces acting on a particle in SHM, and it explains how the system's energy and forces are distributed during the oscillation.

Simple Harmonic Motion (SHM)

SHM is a type of periodic motion in which the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. This concept forms the basis for understanding oscillatory systems, where parameters like amplitude, frequency, and phase are used to describe the periodic behavior of the system.

Angular Frequency

Angular frequency, usually denoted by ?, relates the frequency of oscillation (f) to the rate at which the system cycles through its motion. It is defined as ? = 2?f and plays a crucial role in connecting time-based parameters with spatial attributes of the motion in SHM.

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