Consider an undammed springmass system with mass of 340g Wha

Consider an undammed spring-mass system with mass of 340g. What spring constant will cause it to resonate at a frequency of 6 cycles per second.

Solution

underdamped free motion has the form

x(t)=Aexp(ct2/m)cos(1t+)

1=k/m(c/2m)2

This motion is quasi-periodic. That means the motion isn\'t periodic (since the amplitude is decaying) but the time between successive upcrossings (or downcrossings or maxima or minima) is constant (and, naturally, this time is called the quasi-period).