A coil spring in an oscillating machine runs at between 500 and 1500 rpm (cycles per minute). The spring diameter is 50 mm and the wire diameter is 4 mm. The free length of the spring is 200 mm and the solid length is 80 mm. The ends are squared and held between flat, parallel plates. The spring is made of hard-drawn steel wire. Based on comparing the critical frequency and the range of operating frequencies, is this a good design? Given: For the specific weight of steel, use 77,000 N/m
a. Calculate the number of active coils, Na.
b. Calculate the approximate spring rate, k.
c. Calculate the weight of the spring, W.
d. Calculate the lowest critical frequency, f in cycles per second.
e. Is this an acceptable design?