A particle starts from mean position and performs S.H.M. with period $6$ second. At what time its kinetic energy is $50\%$ of total energy? ($\cos 45^\circ = 1/\sqrt{2}$)

A small sphere oscillates simple harmonically in a watch glass whose radius of curvature is $1.6$ m. The period of Oscillation of the sphere is (Acceleration due to gravity $g = 10 \text{ m/s}^2$)

A wire is under tension of $2$ kg wt and a wave is travelling through it with some speed. Tension in the wire is so increased that the wave travels through it with thrice the original speed. The increase in tension is (in kg wt)

A Pipe open at one end has length $0.8$ m. At the open end of the tube a string $0.5$ m long is vibrating in its first overtone and resonates with fundamental frequency of pipe. If tension in the string is $50$ N, the mass of string is (Neglect end correction) (Speed of sound $= 320$ m/s)