Question

a helical spring fixed by the upper end carries a load of 5kg attached to its lower end .Mass is set into vibration and is measured to make 2 oscillation per seconds .calculate
1.the stiffness of the spring
2.the acceleration at any condition along the spring

Answer 1

First of all Period (T) = time/ number of oscillation
T= 1/2= 0.5s
1. Calculate the stiffness of the spring (k)
But T = 2π√m/k
0.5= 6.284√5/k
0.5/6.284=√5/k
(0.0795)²= (√5/k)²
0.006320= 5/k
K= 5/0.06320
K= 791.1N/m
2. acceleration (a) =Force/mass
a= 50/5= 10m/s²