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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
A spring of force constant $k$ is cut into lengths of ratio $1:2:3$ . They are connected in series and the new force constant is $k'$ . Then they are connected in parallel and force constant is $k''$ . Then $k':k''$ is
A particle with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force $F\sin \omega t$. If the amplitude of the particle is maximum for $\omega = {\omega _1}$ and the energy of the particle is maximum for $\omega = {\omega _2}$, then (where ${\omega _0}$ natural frequency of oscillation of particle)
The force constants of two springs are ${K_1}$ and ${K_2}$. Both are stretched till their elastic energies are equal. If the stretching forces are ${F_1}$ and ${F_2}$, then ${F_1}:{F_2}$ is
Two simple harmonic motions $y_1 = A \sin \omega t$ and $y_2 =A \cos \omega t$ are superimposed on a particle of mass $m.$ The total mechanical energy of the particle is :