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

$A$ body is executing simple harmonic motion of amplitude $a$ and period $T$ about the equilibrium position $x=0$. Large numbers of snapshots are taken at random of this body in motion. The probability of the body being found in a very small interval $x$ to $x+|dx|$ is highest at

Define displacement variable and periodic function.

If the displacement of a particle executing $SHM$ is given by $y = 0.30 \sin(220t + 0.64)$ in meters,then the frequency and maximum velocity of the particle are:

$A$ particle is executing simple harmonic motion with an amplitude $A$. The distance travelled by the particle in half time period is

Define simple harmonic motion. Write important characteristics of simple harmonic motion.

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