A simple pendulum performs simple harmonic motion about x=0 with an amplitude a and time period T. The speed of the pendulum at x= a 2 will be

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?

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 :

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 :

The two-dimensional motion of a particle, described by $\vec{r}=(\hat{i}+2 \hat{j}) A \cos \omega t$ is a/an: A. parabolic path B. elliptical path C. periodic motion D. simple harmonic motion Choose the correct answer from the options given below:

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