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Two identical springs of spring constant $'2k'$ are attached to a block of mass $m$ and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this sytem is ...... .
There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is $T$. If the resultant acceleration becomes $g/4,$ then the new time period of the pendulum is
The plot of velocity $(v)$ versus displacement $(x)$ of a particle executing simple harmonic motion is shown in figure. The time period of oscillation of particle is .........
The displacement of a particle executing SHM is given by $x=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{m}$. The time period of motion is $3.14 \mathrm{~s}$. The velocity of the particle at $\mathrm{t}=0$is_________. $\mathrm{m} / \mathrm{s}$.
Find maximum amplitude for safe $SHM$ (block does not topple during $SHM$) of $a$ cubical block of side $'a'$ on a smooth horizontal floor as shown in figure (spring is massless)
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$. The piston and the cylinder have equal cross sectional area $A$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_ 0$. 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