A particle moves in the x-y plane according t | vedclass

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

Question

(D) Given the position vector: $\overrightarrow{r} = (\widehat{i} + 2\widehat{j}) A \cos \omega t$.Comparing this with $\overrightarrow{r} = x \wideha

Vedclass · Accepted Answer

All of these

Vedclass · Answer

(D) Given the position vector: $\overrightarrow{r} = (\widehat{i} + 2\widehat{j}) A \cos \omega t$.Comparing this with $\overrightarrow{r} = x \widehat{i} + y \widehat{j}$,we get:$x = A \cos \omega t$  $...(1)$$y = 2A \cos \omega t$  $...(2)$From equation $(1)$,we have $\cos \omega t = \frac{x}{A}$. Substituting this into equation $(2)$:$y = 2A \left( \frac{x}{A} \right) = 2x$.Since $y = 2x$ represents a straight line passing through the origin,the motion is on a straight line.Since $x = A \cos \omega t$ and $y = 2A \cos \omega t$ are functions of time involving $\cos \omega t$,the particle oscillates about the origin,which is simple harmonic motion.Since the motion repeats itself after a time interval $T = \frac{2\pi}{\omega}$,the motion is periodic.Therefore,all the given statements are correct.

$A$ particle moves in the $x-y$ plane according to the equation $\overrightarrow{r} = (\widehat{i} + 2\widehat{j}) A \cos \omega t$. The motion of the particle is:

Similar Questions

The displacement of a particle varies according to the relation $x = 3 \sin 100t + 8 \cos^2 50t$. Which of the following is/are correct about this motion?

For a simple harmonic motion represented by the equation $y = 0.30 \sin (220 \, t + 0.64) \ m$,what are the frequency and maximum velocity,respectively?

$A$ simple harmonic motion is represented by $F(t) = 10\sin(20t + 0.5)$. The amplitude of the $S.H.M.$ is $a = $ ....

Define displacement variable and periodic function.

The displacement of a particle is represented by the equation $y = \sin^3 \omega t$. The motion is

Vedclass Test Series

Exam Paper Generator

Online Exam Module