A particle is performing simple harmonic motion with amplitude A and angular velocity ${\omega }$. The ratio of maximum velocity to maximum acceleration is
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The maximum speed of a particle executing $S.H.M.$ is $1\,m/s$ and its maximum acceleration is $1.57\,m/se{c^2}$. The time period of the particle will be .... $\sec$
A particle starts simple harmonic motion from the mean position. Its amplitude is $a$ and total energy $E$. At one instant its kinetic energy is $3E/4.$ Its displacement at that instant is
A brass cube of side $a$ and density $\rho$ is floating in mercury of density $\sigma$. If the cube is displaced a bit vertically, it executes $S.H.M.$ Its time period will be
Two simple harmonic waves having equal amplitudes of $8\,cm$ and equal frequency of $10\,Hz$ are moving along the same direction. The resultant amplitude is also $8\,cm$. The phase difference between the individual waves is $..................$ degree.
A particle of mass m is under the influence of a force $F$ which varies with the displacement $x$ according to the relation $F = - kx + {F_0}$ in which $k$ and ${F_0}$ are constants. The particle when disturbed will oscillate
The instantaneous displacement of a simple pendulum oscillator is given by $x = A\cos \left( {\omega t + \frac{\pi }{4}} \right)$. Its speed will be maximum at time
The amplitude of a particle executing $SHM$ is $3\,cm$. The displacement at which its kinetic energy will be $25 \%$ more than the potential energy is: $.............cm$.
Consider two identical cylinders [each of mass $m$ density $\rho _0$ horizontal cross-section area $s$] in equilibrium, partially submerged in two containers filled with liquids of densities $\rho_1$ and $\rho_2$ as shown in figure. Find the period of small oscillations of this system about its equilibrium. Neglect the changes in the level of liquids in the containers. Neglect mass of the strings. acceleration due to gravity is $g$ . ($v$ is volume of each block)