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

Show that the motion of a particle represented by $y = \sin \omega t - \cos \omega t$ is simple harmonic with a period of $\frac{2\pi}{\omega}$.

$A$ particle moves with simple harmonic motion in a straight line. In the first $\tau \ s$,after starting from rest,it travels a distance $a$,and in the next $\tau \ s$ it travels $2a$ in the same direction. Then:

For a particle performing linear $S.H.M.$,its average speed over one oscillation is ($A=$ amplitude of $S.H.M.$,$n=$ frequency of oscillation) (in $nA$)

The displacement of a particle is given by the relation $x = 4(\cos \pi t + \sin \pi t)$. The amplitude of the particle is

$A$ particle of mass $m$ is under the influence of a force $F = (-kx + F_0) \text{ N}$. The particle,when disturbed,will oscillate

Vedclass Test Series

Exam Paper Generator

Online Exam Module