The uniform stick of mass m length L is pivoted at the centre. In the equilibrium position shown in the figure, the identical light springs have their natural length. If the stick is turned through a small angle $\theta$, it executes SHM. The frequency of the motion is:

(1) $\frac{1}{2\mathrm{\pi }}\sqrt{\frac{6K}{m}}$

(2) $\frac{1}{2\mathrm{\pi }}\sqrt{\frac{3K}{2m}}$

(3) $\frac{1}{2\mathrm{\pi }}\sqrt{\frac{3K}{m}}$

(4) None of these

A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector $\overrightarrow{a}$ is correctly shown in: 

1.		2.
3.		4.

There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is T. If the resultant acceleration becomes g/4, then the new time period of the pendulum is 

(1) 0.8 T

(2) 0.25 T

(3) 2 T

(4) 4 T

­­A man measures the period of a simple pendulum inside a stationary lift and finds it to be T sec. If the lift accelerates upwards with an acceleration $\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ , then the period of the pendulum will be

(1) T

(2) $\frac{\mathrm{T}}{4}$

(3) $\frac{2\mathrm{T}}{\sqrt{5}}$

(4) $2\mathrm{T}\sqrt{5}$

The bob of a pendulum of length l is pulled aside from its equilibrium position through an angle $\theta$ and then released. The bob will then pass through its equilibrium position with a speed v, where v equals

(1) $\sqrt{2\mathrm{gl}(1-\mathrm{sin\theta })}$

(2) $\sqrt{2\mathrm{gl}(1+\mathrm{cos\theta })}$

(3) $\sqrt{2\mathrm{gl}(1-\mathrm{cos\theta })}$

(4) $\sqrt{2\mathrm{gl}(1+\mathrm{sin\theta })}$

In a simple pendulum, the period of oscillation T is related to length of the pendulum l as:
1. $\frac{\mathrm{l}}{T}$= constant
2. $\frac{{\mathrm{l}}^2}{T}$= constant
3. $\frac{\mathrm{l}}{T^2}$= constant
4. $\frac{{\mathrm{l}}^2}{T^2}$= constant

A pendulum has time period T. If it is taken on to another planet having acceleration due to gravity half and mass 9 times that of the earth, then its time period on the other planet will be:

A simple pendulum hanging from the ceiling of a stationary lift has a time period T₁. When the lift moves downward with constant velocity, then the time period becomes T₂. It can be concluded that: 

If the length of a pendulum is made 9 times and mass of the bob is made 4 times, then the value of time period will become:

1. 3T

2. 3/2T

3. 4T

4. 2T

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s² at a distance of 5 m from the mean position. The time period of oscillation is: