A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 \mathrm{~m}$, then the time period of small oscillations will be ____ $s$. $\left[\right.$ take $\left.\mathrm{g}=\pi^2 \mathrm{~ms}^{-2}\right]$

Time period of a simple pendulum will be double, if we

lfa simple pendulum has significant amplitude (up to a factor of $1/e$ of original) only in the period between $t = 0\ s$ to $t = \tau \ s$, then $\tau$ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation ( due to viscous drag) proportional to its velocity with $b$ as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds

What is linear harmonic oscillator ? And what is non-linear oscillator ?

A pendulum suspended from the ceiling of a train has a period $T$ when the train is at rest. When the train travels same distance per unit time, the period of oscillation is

If the metal bob of a simple pendulum is replaced by a wooden bob, then its time period will