Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is $7 : 8$,then the ratio of lengths of the two pendulums will be

The length of the simple pendulum is made $3$ times the original length. If $T$ is its original time period,then the new time period will be:

At what position is the speed of a simple pendulum maximum?

$A$ pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_1$. If the length of the pendulum is doubled and it performs simple harmonic motion with the same angular amplitude as in the first case,its maximum kinetic energy is $K_2$,then:

The linear displacement $x$ of the bob of a simple pendulum from its mean position varies as $x = a \sin \left(\frac{\pi}{\sqrt{2}} t\right)$,where $a$ is its amplitude expressed in meters and $t$ is in seconds. The length of the simple pendulum is (Take $g = \pi^{2} \ m/s^{2}$): (in $m$)

The period of a simple pendulum,whose bob is a hollow metallic sphere,is $T$. The period is $T_1$ when the bob is filled with sand,$T_2$ when it is filled with mercury and $T_3$ when it is half filled with mercury. Which of the following is true?