A car and its suspension system act like a mass-spring system withm= 1200kg and

Question

A car and its suspension system act like a mass-spring system withm= 1200kg and k= 58 kN/m. Its worn-out shock absorbers provide adamping constant b= 230 kg/s. The car hits a pothole that sets itoscillating. How many oscillations will it make before theoscillation amplitude drops to half of its initial value?
Show all work and explainclearly.
Show all work and explainclearly.

Explanation / Answer

As we know,the amplitude of the oscillation at the time t : A =Ao.e^(-bt/m) when the amplitude drops to half of its initialvalue=>   A = Ao/2 =>    t= -ln(1/2)*m/b = 3.616 s the angular velocity of this system : = (k/m -b^2/4m ) = 6.108 rad/s => the period : T = 2/ = 1.0286 s => the number of oscillation : n = t/T = 3.52 oscillations

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