In a stationary lift, time period of a simple pendulum is '$$\mathrm{T}$$'. The lift starts accelerating downwards with acceleration $$\left(\frac{\mathrm{g}}{4}\right)$$, then the time period of the pendulum will be

A particle starts from mean position and performs S.H.M. with period 4 second. At what time its kinetic energy is $$50 \%$$ of total energy?

$$\left(\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)$$

A simple pendulum performs simple harmonic motion about $$\mathrm{x}=0$$ with an amplitude '$$\mathrm{a}$$' and time period '$$T$$'. The speed of the pendulum at $$x=\frac{a}{2}$$ is

Four massless springs whose force constants are $$2 \mathrm{~K}, 2 \mathrm{~K}, \mathrm{~K}$$ and $$2 \mathrm{~K}$$ respectively are attached to a mass $$\mathrm{M}$$ kept on a frictionless plane as shown in figure, If mass $$M$$ is displaced in horizontal direction then frequency of oscillating system is