A simple pendulum of length 1 m and having a bob of mass 100 g is suspended in a car, moving on a circular track of radius 100 m with uniform speed $10 \mathrm{~m} / \mathrm{s}$. If the pendulum makes small oscillation in a radial direction

about its equilibrium position, then its time period can be given by $T=2 \pi / \alpha^{1 / 4}$. The value of $\alpha$ is

[Take, $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

A simple pendulum consists of a small sphere of mass $m$ suspended by a thread of length $l$. The sphere carries a positive charge $q$. The pendulum is allowed to do small oscillations in uniform electric field $E$ with direction vertically upwards. The time period of oscillation is

A body starting at $t=0$ from origin oscillates simple harmonically with a period of 4 s . After what time will its kinetic energy by $75 \%$ of its total energy?

A particle is executing simple harmonic motion in one-dimension. If the amplitude of oscillations is 0.2 cm and if its velocity at the mean position is $5 \mathrm{~m} / \mathrm{s}$, then the angular frequency of the oscillation is