Which of the following equations represents a | vedclass

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

Question

(A) The displacement equation for $SHM$ is given by $x = A \sin(\omega t + \phi)$.Differentiating with respect to time $t$, we get $\frac{dx}{dt} = A

Vedclass · Accepted Answer

$\frac{dx}{dt} = i \omega \sqrt{x^2 - A^2}$

Vedclass · Answer

(A) The displacement equation for $SHM$ is given by $x = A \sin(\omega t + \phi)$.Differentiating with respect to time $t$, we get $\frac{dx}{dt} = A \omega \cos(\omega t + \phi)$.Using the identity $\cos 	heta = \sqrt{1 - \sin^2 	heta}$, we have $\frac{dx}{dt} = A \omega \sqrt{1 - \sin^2(\omega t + \phi)}$.Substituting $\sin(\omega t + \phi) = \frac{x}{A}$, we get $\frac{dx}{dt} = A \omega \sqrt{1 - \frac{x^2}{A^2}}$.Simplifying this, $\frac{dx}{dt} = \omega \sqrt{A^2 - x^2}$.Since $A^2 - x^2 = -(x^2 - A^2)$, we can write $\frac{dx}{dt} = \omega \sqrt{-(x^2 - A^2)}$.Using $i = \sqrt{-1}$, we get $\frac{dx}{dt} = i \omega \sqrt{x^2 - A^2}$.

List-$I$	List-$II$
$A$. $\sin^2 \omega t$	$I$. Periodic but not $SHM$ $(T = 2\pi/\omega)$
$B$. $\sin^3 \omega t$	$II$. Periodic but not $SHM$ $(T = \pi/\omega)$
$C$. $\sin \omega t + \cos \pi \omega t$	$III$. Non-periodic
$D$. $\cos \omega t + \cos 2\omega t$	$IV$. Periodic but not $SHM$ $(T = 2\pi/\omega)$

Which of the following equations represents a simple harmonic motion? $(\omega$ is angular frequency, $A$ is amplitude of oscillation and $i = \sqrt{-1})$

Similar Questions

The mass of a particle is $1\,kg$ and it is moving along the $x-$axis. The period of its small oscillation is $\frac{\pi}{2}$. Its potential energy may be:

Define displacement variable and periodic function.

$A$ function is represented by the equation $y = A \cos \omega t \cos 2\omega t + A \sin \omega t \sin 2\omega t$. Then the nature of the function is:

The graphs in the figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graph best represents the relationship obtained when $y$ is the time?

Vedclass Test Series

Exam Paper Generator

Online Exam Module