Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's centre, where 'R' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period :

If two similar springs each of spring constant K₁ are joined in series, the new spring constant and time period would be changed by a factor :

Y = A sin($$\omega$$t + $$\phi$$₀) is the time-displacement equation of a SHM. At t = 0 the displacement of the particle is $$Y = {A \over 2}$$ and it is moving along negative x-direction. Then the initial phase angle $$\phi$$₀ will be:

Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is :