A small spring has one end welded to a table A bolt is welde

A small spring has one end welded to a table. A bolt is welded to the opposite end of the spring. The bolt weighs 49.2 times 10(-3) kg, or about 1.73 ounces. The spring stiffness is measured to be 857.8 N/m. Initial deflection is 10 mm. Determine: natural frequency 21 Hz period 0.0476 sec Maximum response amplitude. 10 mm Maximum velocity. 1320 mm/s Maximum acceleration 174.24 (10^3) mm/sec^2 If the spring from problem 1 also had 0.11 kg/s of damping, determine Critical damping 12.993 kg/s damping ratio 0.85% is system vibration overdamped, underdamped, or critically damped, (underdamperd)

Solution

Natural Frequency = 1/2 * 1/3.142 * (stiffness/mass)^.5
= 1/2 * 1/3.142 * (857.8/0.0492)^.5
               = 21 Hz

Period = 2 * 3.142 * (mass/stiffness)^.5
= 2 * 3.142 * (0.0492/857.8)^.5
   = 0.0476 sec

Maximum velocity = displacement * (stiffness/mass)^.5
= 10 * (857.8/0.0492)^.5
               = 1320.42 mm/sec