A certain damped oscillator has mass 10 kg period 5 s and

Question

A damped oscillator satisfies the equation

x^·· + 2Kx^· + π²x = 0

where K and Ω are positive constants with K

x = ae^-Kt (cos π_Dt + (K/π_D) sin π_Dt)

where π_D = (π² - K²)^1/2.

Find all the turning points of the function x(t) and show that the ratio of successive maximum values of x is e^-2πK/ΩD.

A certain damped oscillator has mass 10 kg, period 5 s and successive maximum values of its displacement are in the ratio 3 : 1. Find the values of the spring and damping constants α and β.