Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The…

In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency $\omega(t)$ and average amplitude $A(t)$ of the system change with time $t$. Which one of the following options schematically depicts these changes correctly?

Two identical point masses P and Q , suspended from two separate massless springs of spring constants $\mathrm{k}_1$ and $\mathrm{k}_2$, respectively, oscillate vertically. If their maximum speeds are the same, the ratio $\left(A_Q / A_P\right)$ of the amplitude $A_Q$ of mass $Q$ to the amplitude $A_P$ of mass $P$ is :

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to :

If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \mathrm{m}$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are

Let $\omega_1, \omega_2$ and $\omega_3$ be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If $x_1, x_2$ and $x_3$ are their respective angular distances in 1 minute then the factor which remains constant $(k)$ is