A slender bar of mass 12 kg and length of 1 m is pinned to its support at the bar center and coupled to this support by a torsional spring with rate of 1 N·m/rad. The bar end experiences a large transverse force that quickly goes away. The transverse force increased linearly from 0 to 600 N in a quarter second, then decreased linearly back to zero in the next quarter second. Describe the motion of the bar (analytically) for all time t > 0. The bar is initially at rest at its equilibrium position.