$A$ pendulum is swinging in an elevator. Its period will be greatest when the elevator is

To show that a simple pendulum executes simple harmonic motion,it is necessary to assume that

$A$ simple pendulum of length $L$ has mass $M$ and it oscillates freely with amplitude $A$. At the extreme position,its potential energy is $(g =$ acceleration due to gravity$)$

$A$ simple pendulum with a bob of mass $m$ and length $x$ is held in position at an angle $\theta_1$ and then at an angle $\theta_2$ with the vertical. When released from these positions,the speeds with which it passes the lowest position are $v_1$ and $v_2$ respectively. Then,the ratio $\frac{v_1}{v_2}$ is .............

The bob of a pendulum of mass $m$,suspended by an inextensible string of length $L$ as shown in the figure,carries a small charge $q$. An infinite horizontal plane conductor with uniform surface charge density $\sigma$ is placed below it. What will be the time period of the pendulum for small amplitude oscillations?

$A$ simple pendulum of length $L$ and mass (bob) $M$ is oscillating in a plane about a vertical line between angular limits $-\varphi$ and $+\varphi$. For an angular displacement $\theta$ $(|\theta| < \varphi)$,the tension in the string and the velocity of the bob are $T$ and $v$ respectively. Which of the following relations hold good under the above conditions?