The instantaneous displacement of a simple pendulum oscillator is given by $x = A \cos \left( \omega t + \frac{\pi}{4} \right)$. Its speed will be maximum at time

Is the oscillation of a simple pendulum at the centre of the earth possible?

Two masses,both equal to $100\, g$,are suspended at the ends of identical light strings of length $\ell = 1.0\, m$,attached to the same point on the ceiling (see figure). At time $t = 0$,they are simultaneously released from rest,one at angle $\theta_1 = 1^o$,the other at angle $\theta_2 = 2^o$ from the vertical. The masses will collide

If a second's pendulum is moved to a planet where the acceleration due to gravity is $4$ times that on Earth,the length of the second's pendulum on the planet should be made .......... times to keep the time period constant.

The time period of a simple pendulum is $4 \ s$ at a place on the Earth where the acceleration due to gravity is $\pi^2 \ ms^{-2}$. The length of the pendulum in meters is:

The time period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle,which moves without friction down an inclined plane of inclination $\alpha$,is given by: