A particle executes simple harmonic motion an | vedclass

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

Question

(D) Let the equation of motion be $x = A \cos(\omega t + \phi)$. However,for simplicity,we can use $x = A \cos(\omega t)$ if the phase is zero at $t=0

Vedclass · Accepted Answer

$\frac{1}{2\pi t_0} \cos^{-1} \left( \frac{a+c}{2b} \right)$

Vedclass · Answer

(D) Let the equation of motion be $x = A \cos(\omega t + \phi)$. However,for simplicity,we can use $x = A \cos(\omega t)$ if the phase is zero at $t=0$. Given the positions at specific times:$a = A \cos(\omega t_0)$$b = A \cos(2\omega t_0)$$c = A \cos(3\omega t_0)$Using the trigonometric identity $\cos(3	heta) + \cos(	heta) = 2 \cos(2	heta) \cos(	heta)$:$a + c = A \cos(3\omega t_0) + A \cos(\omega t_0) = A [2 \cos(2\omega t_0) \cos(\omega t_0)]$Substitute $b = A \cos(2\omega t_0)$:$a + c = 2b \cos(\omega t_0)$$\cos(\omega t_0) = \frac{a+c}{2b}$$\omega t_0 = \cos^{-1} \left( \frac{a+c}{2b} ight)$Since $\omega = 2\pi f$,we have $2\pi f t_0 = \cos^{-1} \left( \frac{a+c}{2b} ight)$$f = \frac{1}{2\pi t_0} \cos^{-1} \left( \frac{a+c}{2b} ight)$

$A$ particle executes simple harmonic motion and is located at $x = a, b$ and $c$ at times $t_0, 2t_0$ and $3t_0$ respectively. The frequency of the oscillation is

Similar Questions

What is a linear harmonic oscillator and a non-linear harmonic oscillator?

The $S.H.M.$ of a particle is given by the equation $x = 2 \sin \omega t + 4 \cos \omega t$. Its amplitude of oscillation is ........ units.

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:

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 $Hz$):

The displacement of a particle executing simple harmonic motion is given by $x=2 \cos (t)$,where $t$ is the time in seconds. Then,the time period of the particle is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module