Two identical, light, horizontal springs each of force constant k are fixed to opposite rigid walls on a smooth horizontal table. Their free ends are attached to the two sides of a block of mass m so that the block is initially at rest midway between the walls and the springs are unstretched.
(i) If the block is pulled a small distance x to the right and released, show that the net restoring force acting on it is F=−2kx.
(ii) Hence write the differential equation of motion for the block and prove that the motion is simple harmonic.
(iii) Derive the expression for the angular frequency and the time period of the oscillation.
(iv) If k=200Nm−1 and m=0.80kg, calculate the numerical value of the time period.