Statistics Solutions

[Solution Library] (a) Solve the second order ordinary differential equation (d^2x)/(dt^2)+(dx)/(dt)-2x=2t, given the initial conditions x(0)=1, x'(0)=-1. (b) A

Question: (a) Solve the second order ordinary differential equation

\[\frac{{{d}^{2}}x}{d{{t}^{2}}}+\frac{dx}{dt}-2x=2t,\]

given the initial conditions \[x(0)=1,\,\,\,x'(0)=-1.\]

(b) A body of mass 10 kg moves on a horizontal surface, subject to a resistance force of \[R(v)\] Newtons, where v is the instantaneous velocity and the initial velocity is \[v(0)=5\text{ m}{{\text{s}}^{-1}}.\]

  1. Let the resistance force be \[R(v)=v+2{{v}^{2}}\] . Calculate the displacement of the body when it comes to rest.
  2. Suppose the resistance force is changed to \[R(v)=2+0.2{{v}^{3}}.\] Then the distance, x , travelled by the body from its initial position is
\[x=10\int\limits_{v}^{5}{\frac{v}{2+0.2{{v}^{3}}}}dv.\]

Use Simpson’s Rule with four strips to calculate the approximate value of x when \[v=2\text{ m}{{\text{s}}^{-1}}.\] Work to 4 decimal places in all your calculations.

Price: $2.99
Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document


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