The displacement of a particle executing simp | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The given equation is $y = A_{0} + A \sin \omega t + B \cos \omega t$.To find the amplitude,we express the time-dependent part in the form $R \sin

Vedclass · Accepted Answer

$\sqrt{A^{2} + B^{2}}$

Vedclass · Answer

(B) The given equation is $y = A_{0} + A \sin \omega t + B \cos \omega t$.To find the amplitude,we express the time-dependent part in the form $R \sin(\omega t + \phi)$.Let $A = R \cos \phi$ and $B = R \sin \phi$.Then $A^{2} + B^{2} = R^{2} (\cos^{2} \phi + \sin^{2} \phi) = R^{2}$.Thus,$R = \sqrt{A^{2} + B^{2}}$.The equation becomes $y = A_{0} + \sqrt{A^{2} + B^{2}} \sin(\omega t + \phi)$.Here,$A_{0}$ represents the shift in the mean position,and the coefficient of the trigonometric term,$\sqrt{A^{2} + B^{2}}$,represents the amplitude of the oscillation.

The displacement of a particle executing simple harmonic motion is given by
$y = A_{0} + A \sin \omega t + B \cos \omega t$
Then the amplitude of its oscillation is given by

Similar Questions

$A$ particle is executing simple harmonic motion with an amplitude of $2 \,m$. The difference in the magnitudes of its maximum acceleration and maximum velocity is $4$. The time-period of its oscillation and its velocity when it is $1 \,m$ away from the mean position are respectively:

What is oscillatory motion? Give its examples.

$A$ particle is moving with constant angular velocity along the circumference of a circle. Which of the following statements is true?

The equation of motion of a particle of mass $1\,g$ is $\frac{d^2x}{dt^2} + \pi^2x = 0$,where $x$ is displacement (in $m$) from the mean position. The frequency of oscillation is (in $Hz$):

Identify the correct definition.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

The displacement of a particle executing simple harmonic motion is given by$y = A_{0} + A \sin \omega t + B \cos \omega t$Then the amplitude of its oscillation is given by