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 position co-ordinates of a particle moving in a $3D$ coordinate system is given by

$x=a\cos \mathrm{\omega }\mathrm{t}$

$y=a\sin \omega t$

and $z=a\omega t$

The speed of the particle is:

A particle moves in the $xy$ -plane under the action of superposition of two simple harmonic vibrations. The resultant displacement of the particle is governed by the equation.

$\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{2xy}{ab}cos\mathrm{\alpha }=si{n}^2\mathrm{\alpha }$

where $a\mathit{\text{,}}\mathit{ }b$ and $\mathrm{\alpha }$ are positive constants. The particle trajectory $y\left(x\right)$ is linear with a negative slope for

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $\mathit{\text{M}}$. The piston and the cylinder have equal cross-sectional area $\mathit{\text{A}}$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $M_0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[Assume the system is in space.]