The motion of a particle varies with time acc | vedclass

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

Question

(C) Given the equation of motion: $y = a(\sin \omega \,t + \cos \omega \,t)$.We can rewrite this by multiplying and dividing by $\sqrt{2}$:$y = a\sqrt

Vedclass · Accepted Answer

The motion is $S.H.M.$ with amplitude $a\sqrt{2}$

Vedclass · Answer

(C) Given the equation of motion: $y = a(\sin \omega \,t + \cos \omega \,t)$.We can rewrite this by multiplying and dividing by $\sqrt{2}$:$y = a\sqrt{2} \left( \frac{1}{\sqrt{2}} \sin \omega \,t + \frac{1}{\sqrt{2}} \cos \omega \,t \right)$.Using the trigonometric identity $\sin(A+B) = \sin A \cos B + \cos A \sin B$,where $\sin 45^\circ = \frac{1}{\sqrt{2}}$ and $\cos 45^\circ = \frac{1}{\sqrt{2}}$:$y = a\sqrt{2} (\sin \omega \,t \cos 45^\circ + \cos \omega \,t \sin 45^\circ)$.$y = a\sqrt{2} \sin(\omega \,t + 45^\circ)$.This is the standard equation of Simple Harmonic Motion $(S.H.M.)$,which is $y = A \sin(\omega \,t + \phi)$,where the amplitude $A = a\sqrt{2}$.

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

Similar Questions

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

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

Define simple harmonic motion and explain it.

$A$ body is executing simple harmonic motion of amplitude $a$ and period $T$ about the equilibrium position $x=0$. Large numbers of snapshots are taken at random of this body in motion. The probability of the body being found in a very small interval $x$ to $x+|dx|$ is highest at

What is displacement? Explain its general meaning by giving examples.

Vedclass Test Series

Exam Paper Generator

Online Exam Module