Two simple pendulums have time periods T and . They start vibrating at the same instant from the mean position in the same phase. The phase difference between them when bigger pendulum completes one oscillation will be:
1.
2.
3.
4.
A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector \(\vec a\) 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 small sphere carrying a charge ‘q’ is hanging in between two parallel plates by a string of length L. Time period of pendulum is T0. When parallel plates are charged, the electric field between the plates is E and time period changes to T. The ratio T/T0 is equal to
(1) (2)
(3) (4) None of these
1. | \(\pi \) | 2. | \(2 \pi \) |
3. | \(4 \pi \) | 4. | \(6 \pi\) |
The uniform stick of mass m length \(\text L\) 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 , it executes SHM. The frequency of the motion is:
1. \(\frac{1}{2 \pi} \sqrt{\frac{6 K}{m}} \)
2. \(\frac{1}{2 \pi} \sqrt{\frac{3 K}{2 m}} \)
3. \(\frac{1}{2 \pi} \sqrt{\frac{3 K}{m}} \)
4. None of these
A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude?
(1)
(2)
(3)
(4)
Which of the following figure represents damped harmonic motion?
(i) | |
(ii) | |
(iii) | |
(iv) |
1. (i) and (ii)
2. (iii) and (iv)
3. (i), (ii), (iii), and (iv)
4. (i) and (iv)
1. | the motion is oscillatory but not SHM. |
2. | the motion is SHM with an amplitude \(a\sqrt{2}\). |
3. | the motion is SHM with an amplitude \(\sqrt{2}\). |
4. | the motion is SHM with an amplitude \(a\). |