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In the arrangement, spring constant $k$ has value $2\,N\,m^{-1}$ , mass $M = 3\,kg$ and mass $m = 1\,kg$ . Mass $M$ is in contact with a smooth surface. The coefficient of friction between two blocks is $0.1$ . The time period of $SHM$ executed by the system is
The length of a seconds pendulum at a height $h=2 R$ from earth surface will be.(Given: $R =$ Radius of earth and acceleration due to gravity at the surface of earth $g =\pi^{2}\,m / s ^{-2}$ )
The displacement of an oscillating particle varies with time (in seconds) according to the equation $y (cm) = sin \frac{\pi }{2}\left( {\frac{t}{2} + \frac{1}{3}} \right)$. The maximum acceleration of the particle is approximately ..... $cm/s^2$
The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended , the period of oscillation will now be