The motion of a particle represented by y = s | vedclass

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

Question

(B) Given equation: $y = \sin \omega t - \cos \omega t$.Multiply and divide by $\sqrt{2}$:$y = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin \omega t - \fra

Vedclass · Accepted Answer

$S.H.M.$ with period $\frac{2\pi}{\omega}$,amplitude $\sqrt{2}$

Vedclass · Answer

(B) Given equation: $y = \sin \omega t - \cos \omega t$.Multiply and divide by $\sqrt{2}$:$y = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin \omega t - \frac{1}{\sqrt{2}} \cos \omega t \right)$.Using the trigonometric identity $\sin(A - B) = \sin A \cos B - \cos A \sin B$,we can write:$y = \sqrt{2} \sin \left( \omega t - \frac{\pi}{4} \right)$.This is the standard form of a Simple Harmonic Motion ($S$.$H$.$M$.) equation,$y = A \sin(\omega t + \phi)$,where $A$ is the amplitude and $\omega$ is the angular frequency.Comparing the equations,the amplitude $A = \sqrt{2}$.The time period $T$ is given by $T = \frac{2\pi}{\omega}$.Thus,the motion is $S.H.M.$ with period $\frac{2\pi}{\omega}$ and amplitude $\sqrt{2}$.

The motion of a particle represented by $y = \sin \omega t - \cos \omega t$ is

Similar Questions

$A$ particle is performing $SHM$ according to the equation $x = (3\, cm) \sin \left( \frac{2\pi t}{18} + \frac{\pi}{6} \right)$ where $t$ is in seconds. The distance travelled by the particle in $36\, s$ is ..... $cm$.

What is a linear harmonic oscillator? And what is a non-linear oscillator?

The displacement of a particle varies with time according to the relation $x = a \sin \omega t + b \cos \omega t$.

What is periodic motion? Give its examples.

Which of the following equations does not represent a simple harmonic motion?

Vedclass Test Series

Exam Paper Generator

Online Exam Module