In a spring test, Eddie releases the spring from rest at a height of 20 cm beyon
ID: 3120757 • Letter: I
Question
In a spring test, Eddie releases the spring from rest at a height of 20 cm beyond the spring's natural length (i.e. y(0) = 20). He finds that the resulting vibration has a period of 1 s and that the amplitude of the vibration halves after 3 s ("half-life"). From his knowledge of damped springs, he also knows that the spring should behave according to the equation y(t) = Ae^-bt COS(ct). Solve the function parameters A, b and c using hand working, and hence write down the equation y(t) for the spring he tested.Explanation / Answer
since half life of vibration is 3 sec;
So b = ln(2)/3 per sec; or
b=0.693/3 per sec; =0.231 /sec;
A = 20cm i.e. maximum length from equilibrium;
and C = 2 pi/T = 2pi /sec;