Superposition of Two or More SHM

Two identical sinusoidal waves each of amplitude $10 \mathrm{mm},$, with a phase difference of $90°$ are travelling with the same direction in a string. The amplitude of the resultant wave is

Two particles $\text{'}\mathrm{P}\text{'}$ and $\text{'}\mathrm{Q}\text{'}$ describe SHM of same amplitude $\text{'}a\text{'}$ and same frequency $\text{'}f\text{'}$ along the same straight line. The maximum distance between the two particles is $a\sqrt{2}.$ The phase difference between the particle is

The superposition of two S.H.M is given by $x=\left(5\mathrm{cm}\right) \sin \left(100\mathrm{\pi t}+\frac{\mathrm{\pi }}{3}\right)$. Find the angular frequency of the wave?

The resultant of two simple harmonic motions of the same frequency and unequal amplitudes but differing in phase by, $\frac{\mathrm{\pi }}{2}$ is 

The motion of a particle is given, $x=A\sin \omega t+B\cos \omega t$. The motion of the particle is

The position of a particle with respect to origin varies according to the relation $x=3\sin 100t+8{\cos }^{2}50t$. Which of the following is correct about this motion?

The superposition of two S.H.M is given by $x=\left(5\mathrm{cm}\right) \sin \left(100\mathrm{\pi t}+\frac{\mathrm{\pi }}{3}\right)$. Find the angular frequency of the wave?

The motion of a particle is given by the equation $\mathrm{x}=\mathrm{Asin\omega t}+\mathrm{Bcos\omega t}$ is

Select the correct statement about a particle subjected to two simple harmonic motions along $x$ and $y$ directions according to $x=3\sin 100\pi t$ and $y=4\sin 100\pi t$.

A particle is subjected to two simple harmonic motions simultaneously along x and y directions according to equation $\text{x}=\text{3 sin 100 }\pi \text{t ; y}=\text{4 sin 100 }\pi \text{t}$, then-

A particle is subjected to two simple harmonic motions long $X$ -axis while other is along a line making angle ${45}^o$ with the $X$ -axis. The two motions are given by $x=x_0\sin \omega t$ and $s=s_0\sin \omega t.$

The amplitude of resultant motion is

Four waves are represented by $y_1=A_1\mathrm{sin\pi }t$ , $y_2{=A}_2\sin \left(\mathrm{\pi }t+\frac{\mathrm{\pi }}{2}\right)$, $y_3=A_1\sin \left(2\mathrm{\pi }t+\frac{\mathrm{\pi }}{2}\right)$ and $y_4=A_2\sin \left(\mathrm{\pi }t-\frac{\mathrm{\pi }}{3}\right)$ . Interference will happen with-

A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, $x_1\left(t\right)=A\mathrm{s}\mathrm{i}\mathrm{n}\omega t$ and $x_2\left(t\right)=A\mathrm{s}\mathrm{i}\mathrm{n}\left(\omega t+\frac{2\pi }{3}\right)$.  Adding a third sinusoidal displacement $x_3\left(t\right)=B\mathrm{s}\mathrm{i}\mathrm{n}\left(\omega t+\varphi \right)$ brings the mass to a complete rest. The values of B and $\varphi$

When two displacements represented by ${\mathrm{y}}_1=\mathrm{a}\mathrm{ }\mathrm{s}\mathrm{i}\mathrm{n}\left(\mathrm{\omega }\mathrm{t}\right)$ and ${\mathrm{y}}_2=\mathrm{b}\cos \left(\mathrm{\omega }\mathrm{t}\right)$ are superimposed the motion is:

The displacement equation of a particle is $\mathrm{x}=3\sin 2\mathrm{t}+4\cos 2\mathrm{t}$. The amplitude & maximum velocity will be respectively -

Two unlike charges, of same magnitude $Q$, are placed at a distance $d$. The intensity of the electric field, at the mid point of the line joining the two charges, is

The displacement y of a particle is given by $y=4{\cos }^2\left(\frac{t}{2}\right)\sin \left(1000t\right)$. This expression may be considered to be a result of the superposition of how many simple harmonic motions?

A travelling wave represented by $y=a\sin \left(\omega t-kx\right)$ is superimposed on another wave represented b$y=a\sin \left(\omega t+kx\right)$. The resultant is

If two waves of the same frequency and amplitude respectively on superposition produce a resultant disturbance of the same amplitude, the waves differ in phase by

Two simple harmonic motions act on a particle. These harmonic motions are

$x=A\cos \left(\omega t+\alpha +\frac{\pi }{2}\right)$ and $Y=A\cos (\omega t+\alpha )$.