Given data
*The given mass of the car is m = 1610 kg
*The given effective force constant is k = 5.75 × 10^4 N/m
(a)
The formula for the period of oscillation of a 1610 kg car is given as
[tex]T=2\pi\sqrt[]{\frac{m}{k}}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} T=2\times3.14\times\sqrt[]{\frac{1610}{5.75\times10^4}} \\ =1.05\text{ s} \end{gathered}[/tex]Hence, the time period of oscillation of a 1610 kg car is T = 1.05 s
(b)
As from the given data, the amplitude of the oscillation of the car decreases by a factor of 5.00. Then, the expression for the amplitude of the oscillation, and the damping constant (b) is calculated as
[tex]A=A_0e^{-\frac{bt}{2m}}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} \frac{A_0}{5.0}=A_0e^{-\frac{bt}{2m}} \\ bt=2m\ln (5.0)_{} \\ b(\frac{T}{2})=2m\ln (5.0) \\ b=\frac{4m\ln (5.0)}{T} \\ =\frac{4\times1610\times\ln (5.0)}{1.05} \\ =9871.2\text{ kg/s} \end{gathered}[/tex]Hence, the damping constant is b = 9871.2 kg/s
