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A rod of mass $‘M’$ and length $‘2L’$ is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of $‘m’$ are attached at distance $‘L/2’$ from its centre on both sides, it reduces the oscillation frequency by $20\%$. The value of ratio $m/M$ is close to
The equation of an $S.H.M.$ with amplitude $A$ and angular frequency $\omega$ in which all the distances are measured from one extreme position and time is taken to be zero at the other extreme position is ...
A particle excutes $SHM$ on a straight line path. The amplitude of oscillation is $2\,cm$. When the displacement of the particle from the mean position is $1\,cm$, the numerical value of magnitude of acceleration is equal to the numerical value of magnitude of velocity. The frequency of $SHM$ is (in $second^{-1}$)
Consider a one-dimensional potential $V(x)$ as shown in the figure below. A classical particle of mass $m$ moves under its influence and has total energy $E$ as shown below. The motion is
A particle at the end of a spring executes simple harmonic motion with a period ${t_1}$, while the corresponding period for another spring is ${t_2}$. If the period of oscillation with the two springs in series is $T$, then
Two simple harmonic motions are represented by equations ${y_1} = 4\,\sin \,\left( {10t + \phi } \right)$ and ${y_2} = 5\,\cos \,10\,t$ What is the phase difference between their velocities?
A $2\, Kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi ^2 N/m$ attached to $2\, Kg$ block at rest kept on a smooth floor, the velocity of the rear $2\, kg$ block after it separates from the spring will be ..... $m/s$