If two SHM's are given by the equation y1=0.1 sin[πt+(π/ 3)] and y2=0.1 cosπt, then the phase di

step 1 In this question, we will learn about some basic concept of the oscillation and waves. The quest

If two SHM's are given by the equation y1=0.1 sin[πt+(π/ 3)]...

If two SHM's are given by the equation $\mathrm{y}_{1}=0.1 \sin [\pi \mathrm{t}+(\pi / 3)]$ and $\mathrm{y}_{2}=0.1 \cos \pi \mathrm{t}$, then the phase difference between the velocity of particle 1 and 2 is $\ldots \ldots \ldots$ (A) $\pi / 6$ (B) $-\pi / 3$ (C) $\pi / 3$ (D) $-\pi / 6$

If two SHM's are given by the equation $\mathrm{y}_{1}=0.1 \sin [\pi \mathrm{t}+(\pi / 3)]$ and $\mathrm{y}_{2}=0.1 \cos \pi \mathrm{t}$, then the phase
difference between the velocity of particle 1 and 2 is $\ldots \ldots \ldots$
(A) $\pi / 6$
(B) $-\pi / 3$
(C) $\pi / 3$
(D) $-\pi / 6$

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Key Concepts

Relationship between Displacement and Velocity in SHM

In SHM, the velocity is the derivative of displacement with respect to time, resulting in a phase shift of ?/2 (or 90°). This means that the velocity reaches its maximum when the displacement is zero, and this intrinsic phase difference is critical when comparing the dynamics between position and velocity or between two different particle motions.

Simple Harmonic Motion (SHM)

SHM describes oscillatory motion in which the restoring force is proportional to the displacement. It is typically modeled using sine or cosine functions that oscillate periodically with a constant amplitude and angular frequency, encapsulating the fundamental nature of periodic physical phenomena.

Phase Constant and Phase Difference

The phase constant in an oscillatory function determines the initial angular offset of the motion on its time cycle, while the phase difference compares the shift between two oscillatory functions. This difference is crucial in understanding how two oscillations are synchronized or out-of-step relative to one another.

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