A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60$$^\circ$$ to the vertical will be (g = 10 m/s²) ____________ m/s.

A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $${1 \over a}$$s. The value of 'a' to the nearest integer is _________.

Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is T_b/T_a = $$\sqrt x $$, where value of x is ___________. (Round off to the Nearest Integer)

A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of the particle when its speed is half of maximum speed is $${{\sqrt x a} \over 2}$$. The value of x is __________.