A spring with the Hooke's law constant k = 1 kg/s² has an oscillating object of mass 4kg attached to it. There is an external force F(t) = cos(wot) applied to the object and no damping force. Find the frequency wo of the external force F(t) which would yield a resonance, that is determine wo for which the equation the amplitude of the moving object increases without bound.

A block of mass m hangs from a spring with a spring constant k. The block is initially held so that the spring is unstretched. If the natural circular frequency of the system is 10 radians/sec, how many cycles of vibration will the block experience in five seconds after it is released?

If a product deflects its cushion by 5 mm, at rest, find the natural frequency of the system.

A mass weighing 1/4 kg. is attached to a spring with stiffness k = 16 N/m. The mass is displaced 1/2 m. to the right of the equilibrium position and given a rightward velocity of 1 m/sec. Neglect damping and external forces. Find y(t), A, phi, omega, the period P and the first time (t>0) the mass passes through equilibrium.