Solutions
From the picture it can be seen that the damping decreases the frequency of the oscillations.
In[23]:=
Out[24]=
Out[25]=
Out[27]=
![(*4.1*)Clear[m, k, x, t, γ, s] ; x_1 = Part[DSolve[{m x''[t] + k x[t] & ... γ = 0.3 ; s = 0.1 ; Plot[{x[t]/.x_1, x[t]/.x_2}, {t, 0, 30}, ImageSize500]](../HTMLFiles/ex06_solutions_29.gif)
![x[t] s Cos[(k^(1/2) t)/m^(1/2)]](../HTMLFiles/ex06_solutions_30.gif){kind=small}
![x[t] (^(-(t γ)/(2 m)) s ((-4 k m + γ^2)^(1/2) Cosh[(t (-4 k m + & ... ^2)^(1/2))/(2 m)] + γ Sinh[(t (-4 k m + γ^2)^(1/2))/(2 m)]))/(-4 k m + γ^2)^(1/2)](../HTMLFiles/ex06_solutions_31.gif)
![[Graphics:../HTMLFiles/ex06_solutions_32.gif]](../HTMLFiles/ex06_solutions_32.gif)
