The function of time representing a simple ha | vedclass

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

Question

(D) The time period of a simple harmonic motion $(SHM)$ is given by $T = \frac{2\pi}{\omega'}$,where $\omega'$ is the angular frequency of the $SHM$.G

Vedclass · Accepted Answer

$3 \cos \left(\frac{\pi}{4}-2 \omega t\right)$

Vedclass · Answer

(D) The time period of a simple harmonic motion $(SHM)$ is given by $T = \frac{2\pi}{\omega'}$,where $\omega'$ is the angular frequency of the $SHM$.Given $T = \frac{\pi}{\omega}$,we have $\frac{\pi}{\omega} = \frac{2\pi}{\omega'}$,which implies $\omega' = 2\omega$.We need to find the function that represents $SHM$ with an angular frequency of $2\omega$.For option $(C)$: $\sin^2(\omega t) = \frac{1 - \cos(2\omega t)}{2} = \frac{1}{2} - \frac{1}{2}\cos(2\omega t)$. This represents a constant shift plus an $SHM$ with angular frequency $2\omega$.For option $(D)$: $3 \cos \left(\frac{\pi}{4} - 2\omega t\right) = 3 \cos \left(2\omega t - \frac{\pi}{4}\right)$. This is a standard $SHM$ equation $x(t) = A \cos(\omega' t + \phi)$ with angular frequency $\omega' = 2\omega$.Both $(C)$ and $(D)$ have the correct frequency,but $(D)$ is a pure $SHM$ function,whereas $(C)$ includes a constant term.

The function of time representing a simple harmonic motion with a period of $\frac{\pi}{\omega}$ is :

Similar Questions

$A$ system exhibiting $S.H.M.$ must possess

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:

The radius of the circle,the period of revolution,the initial position,and the sense of revolution are indicated in the figure. The $y$-projection of the radius vector of the rotating particle $P$ is:

Who decides the characteristics of $SHM$?

The displacement equation of a particle is $x = 3\sin 2t + 4\cos 2t$. The amplitude and maximum velocity will be respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module