Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is:

Two springs are connected to block of mass M placed on a frictionless surface as shown below. If both the springs have a spring constant $$k$$​. the frequency of oscillation of the block is:

Two masses $$\text m_1$$​ and $$\text m_2$$​ are connected by a massless spring of spring constant k. The system is free to oscillate along the length of spring. The system oscillates with a frequency:

The period of a pendulum is given as $$T = 2\pi \sqrt{\frac{l}{g}}$$​ where g = 9.81 m/s² and π = 3.1416. The period of a pendulum of length 1 m correct to the first place of decimal in seconds is