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The particle executing simple harmonic motion has a kinetic energy $K_0cos^2 \omega t$. The maximum values of the potential energy and the total energy are respectively
Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated in the figure. The simple harmonic motion of the $x-$ projection of the radius vector of the rotating particle $P$ is
A load of mass $m$ falls from a height $h$ on to the scale pan hung from the spring as shown in the figure. If the spring constant is $k$ and mass of the scale pan is zero and the mass $m$ does not bounce relative to the pan, then the amplitude of vibration is
In the figure, ${S_1}$ and ${S_2}$ are identical springs. The oscillation frequency of the mass $m$ is $f$. If one spring is removed, the frequency will become
A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs of equal spring constants $k$. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $\theta$ in one direction and released. The frequency of oscillation is
A mass $m$ is attached to two springs of same force constant $K$, as shown in following four arrangements. If $T_1, T_2, T_3$ and $T_4$ respectively be the time periods of oscillation in the following arrangements, in which case time period is maximum?
For a particle executing simple harmonic motion, the kinetic energy $K$ is given by $K = {K_o}{\cos ^2}\omega t$. The maximum value of potential energy is