Which of the following functions represents a | vedclass

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

Question

(A) function represents simple harmonic motion $(S.H.M.)$ if it satisfies the differential equation $\frac{d^2x}{dt^2} + \omega^2 x = 0$.Option $A$: $

Vedclass · Accepted Answer

$\sin \omega t - \cos \omega t$

Vedclass · Answer

(A) function represents simple harmonic motion $(S.H.M.)$ if it satisfies the differential equation $\frac{d^2x}{dt^2} + \omega^2 x = 0$.Option $A$: $x = \sin \omega t - \cos \omega t$. This can be written as $x = \sqrt{2} [\frac{1}{\sqrt{2}} \sin \omega t - \frac{1}{\sqrt{2}} \cos \omega t] = \sqrt{2} \sin(\omega t - \frac{\pi}{4})$. This is a standard $S.H.M.$ equation.Option $B$: $x = \sin^2 \omega t = \frac{1 - \cos 2\omega t}{2}$. This represents motion with a constant shift and frequency $2\omega$,which is not simple harmonic.Options $C$ and $D$: These are superpositions of two different frequencies ($\omega$ and $2\omega$),which result in periodic motion but not simple harmonic motion.Therefore,the correct option is $A$.

Which of the following functions represents a simple harmonic oscillation?

Similar Questions

The equation of an $S.H.M.$ with amplitude $A$ and angular frequency $\omega$ in which all distances are measured from one extreme position and time is taken to be zero at the other extreme position is ...

What is the ratio between the distance travelled by the oscillator in one time period and the amplitude?

The motion of a particle varies with time according to the relation $y = a(\sin \omega t + \cos \omega t)$.

The displacement $x$ (in metre) of a particle in simple harmonic motion is related to time $t$ (in seconds) as $x = 0.01 \cos \left( \pi t + \frac{\pi}{4} \right)$. The frequency of the motion will be

$A$ particle free to move along the $x$-axis has potential energy given by $U(x) = k[1 - \exp(-x^2)]$ for $-\infty \le x \le +\infty$,where $k$ is a positive constant of appropriate dimensions. Then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module