When two displacements represented by y_1 = a | vedclass

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

Question

(C) Given the two displacements:$y_1 = a \sin(\omega t)$$y_2 = b \cos(\omega t) = b \sin(\omega t + \frac{\pi}{2})$The resultant displacement $y = y_1

Vedclass · Accepted Answer

simple harmonic with amplitude $\sqrt{a^2 + b^2}$

Vedclass · Answer

(C) Given the two displacements:$y_1 = a \sin(\omega t)$$y_2 = b \cos(\omega t) = b \sin(\omega t + \frac{\pi}{2})$The resultant displacement $y = y_1 + y_2$ is given by:$y = a \sin(\omega t) + b \cos(\omega t)$To find the amplitude,we can write this in the form $y = A \sin(\omega t + \phi)$,where the resultant amplitude $A$ is:$A = \sqrt{a^2 + b^2 + 2ab \cos(\frac{\pi}{2})}$Since $\cos(\frac{\pi}{2}) = 0$,the amplitude is:$A = \sqrt{a^2 + b^2}$Thus,the resultant motion is simple harmonic with an amplitude of $\sqrt{a^2 + b^2}$.

When two displacements represented by $y_1 = a \sin(\omega t)$ and $y_2 = b \cos(\omega t)$ are superimposed,the motion is

Similar Questions

Two simple harmonic motions are given by $x_{1} = a \sin \omega t + a \cos \omega t$ and $x_{2} = a \sin \omega t + \frac{a}{\sqrt{3}} \cos \omega t$. The ratio of the amplitudes of the first and second motion and the phase difference between them are respectively:

The amplitude of the vibrating particle due to the superposition of two $SHMs$,$y_1 = \sin \left( \omega t + \frac{\pi}{3} \right)$ and $y_2 = \sin \omega t$ is:

Four simple harmonic vibrations:
$y_1 = 8 \cos(\omega t)$;
$y_2 = 4 \cos(\omega t + \frac{\pi}{2})$;
$y_3 = 2 \cos(\omega t + \pi)$;
$y_4 = 1 \cos(\omega t + \frac{3\pi}{2})$,
are superposed on each other. The resulting amplitude and phase are respectively:

Two particles are executing simple harmonic motion of the same amplitude $A$ and frequency $\omega$ along the $x$-axis. Their mean positions are separated by a distance $X_0$ $(X_0 > A)$. If the maximum separation between them is $(X_0 + A)$,the phase difference between their motions is:

The $S.H.M.$ of a particle is given by the equation $y = 3\sin \omega t + 4\cos \omega t$. The amplitude is

Vedclass Test Series

Exam Paper Generator

Online Exam Module