For particles A and B executing S.H.M., the equation for...

For particles $\mathrm{A}$ and $\mathrm{B}$ executing S.H.M., the equation for displacement is given by $\mathrm{y}_{1}=0.1 \sin (100 \mathrm{t}+\mathrm{p} / 3)$ and $\mathrm{y}_{2}=0.1$ cos pt respectively. The phase difference between velocity of particle $\mathrm{A}$ with respect to that of $\mathrm{B}$ is $\ldots \ldots$ $(\mathrm{A})-(\pi / 3)$ (B) $(\pi / 6)$ (C) $-(\pi / 6)$ (D) $(\pi / 3)$

For particles $\mathrm{A}$ and $\mathrm{B}$ executing S.H.M., the equation for displacement is given by $\mathrm{y}_{1}=0.1 \sin (100 \mathrm{t}+\mathrm{p} / 3)$ and
$\mathrm{y}_{2}=0.1$ cos pt respectively. The phase difference between velocity of particle $\mathrm{A}$ with respect to that of $\mathrm{B}$ is $\ldots \ldots$
$(\mathrm{A})-(\pi / 3)$
(B) $(\pi / 6)$
(C) $-(\pi / 6)$
(D) $(\pi / 3)$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Displacement and Velocity in SHM

In SHM, the displacement of a particle is often expressed as a sinusoidal function of time, and the velocity is the derivative of the displacement with respect to time. Differentiation introduces a phase shift, typically of ?/2 radians, meaning that the velocity reaches its maximum when the displacement passes through zero.

Phase Difference

Phase difference in oscillatory motion refers to the amount by which one waveform is ahead or behind another. It is a critical concept when comparing two or more sinusoidal functions, such as the displacement or velocity of oscillating particles, and it determines how the peaks and troughs of the functions align relative to each other.

Simple Harmonic Motion (SHM)

Simple Harmonic Motion is a type of oscillatory motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. This results in sinusoidal displacement and velocity functions over time, which are fundamental in understanding periodic systems in physics.

Transcript

Please give Ace some feedback