The displacement of a particle varies according to the relation $x = 3 \ sin\ 100t + 8\ cos^2\ 50t$ . Which of the following is incorrect about this motion
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Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be
In the given figure, a mass $M$ is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is $k$. The mass oscillates on a frictionless surface with time period $T$ and amplitude $A$. When the mass is in equilibrium position, as shown in the figure, another mass $m$ is gently fixed upon it. The new amplitude of oscillation will be
The height of liquid column in a $U$ tube is $0.3$ meter. If the liquid in one of the limbs is depressed and then released, then the time period of liquid column will be $.......\,sec$
A load of mass $m$ falls from a height $h$ on to the scale pan hung from the spring as shown in the figure. If the spring constant is $k$ and mass of the scale pan is zero and the mass $m$ does not bounce relative to the pan, then the amplitude of vibration is