A block having a mass of 500 g is tied to a thread having a length of 35 cm. The block is pulled sideward such that the thread makes an angle of 6° with respect to vertical and then released. The block oscillates with a damping constant of 0.005 kg/s. Determine the number of oscillations after 30 s and also the fraction of energy lost.

What is the damping constant b for a 76 g mass oscillating on a vertical spring with a spring constant of 116 N/m in a cylinder filled with oil, if the initial displacement is 6.0 cm and the amplitude reduces to 3.0 cm after 3.6 s? Assume no buoyant forces.

What is the maximum compression of the bumper of a vehicle of mass 1400 kg, equipped with an 'ImpactGuard' system having a spring constant of 420,000 N/m, when the vehicle collides with a barrier at a speed of 3.0 m/s?

A mechanical seismograph, initially critically damped, measures ground vibrations using a spring system. After several years of operation, it is observed that the amplitude of the system's oscillations reduces to 7% of their initial value after 4 cycles following a disturbance. Estimate the new damping constant (in percent) with respect to the original one of the spring system.