Two S.H.Ms. are represented by equations $$\mathrm{y}_1=0.1 \sin \left(100 \pi \mathrm{t}+\frac{\pi}{3}\right)$$ and $$\mathrm{y}_2=0.1 \cos (100 \pi \mathrm{t})$$ The phase difference between the speeds of the two particles is
A spring has a certain mass suspended from it and its period for vertical oscillations is '$$T_1$$'. The spring is now cut in to two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now '$$\mathrm{T}_2$$'. The ratio $$\mathrm{T}_1 / \mathrm{T}_2$$ is
A particle is vibrating in S.H.M. with an amplitude of $$4 \mathrm{~cm}$$. At what displacement from the equilibrium position is its energy half potential and half kinetic?
A rubber ball filled with water, having a small hole is used as the bob of a simple pendulum. The time period of such a pendulum