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) $\mathrm{b}$ (C) $c$ (D) $\mathrm{d}$ Statement $-1:$ For a particle executing SHM, the amplitude and phase is decided by its initial position and initial velocity. Statement $-2:$ In a SHM, the amplitude and phase is dependent on the restoring force. (A) a (B) $b$ (C) $\mathrm{c}$ (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) $\mathrm{b}$
(C) $c$
(D) $\mathrm{d}$
Statement $-1:$ For a particle executing SHM, the amplitude and phase is decided by its initial position and initial velocity. Statement $-2:$ In a SHM, the amplitude and phase is dependent on the restoring force.
(A) a
(B) $b$
(C) $\mathrm{c}$
(D) $\mathrm{d}$

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Key Concepts

Amplitude and Phase

Amplitude refers to the maximum extent of displacement from the equilibrium position, while phase indicates the initial angular state of the oscillation. Both parameters are dependent on the initial conditions of the system, defining the specific characteristics of the oscillatory motion over time.

Restoring Force

The restoring force in simple harmonic motion is the force responsible for pulling the system back towards its equilibrium position. It is generally proportional to the displacement and is a critical component that gives rise to the sinusoidal nature of the oscillations in SHM.

Simple Harmonic Motion

Simple harmonic motion is a type of periodic oscillatory motion where the restoring force is directly proportional to the displacement of the object from its equilibrium position, following a sinusoidal pattern. This concept is central to the analysis of systems like springs, pendulums, and other physical oscillators.

Initial Conditions

Initial conditions in simple harmonic motion, such as the particle's initial position and velocity, are crucial because they determine the specific parameters of the motion, including the amplitude and phase of oscillation. These conditions allow one to uniquely define the motion of an oscillator.

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