Understanding Dynamics: Solving a Tricky Example

[robcowlam]

HI guys,

Im having some trouble with a dynamics question, I am only looking at a worked example however I can't see where the final answer comes from.
The problem is sample 3/5 on http://www.eng.auburn.edu/~marghitu/MECH2110/Dynamics/D2_1_examples.pdf
I follow the working until the line after "which becomes" I cannot see why the integral becomes
F/k [sin(kt)+Uk(cos kt - 1)] - mgt =
mv
rather than:

F/k [sin(kt)+Uk(cos kt)] - mgt =
mv

Its probably just something small but I can't figure it out,
Can anybody help me out?

Thanks!

 

[nvn]

robcowlam: That is normal calculus (definite integration). Thus, integral[-mu*F*sin(k*t)*dt], integrated from t = 0 to t, is equal to -mu*(F/k)*{-cos(k*t) - [-cos(k*0)]} = -mu*(F/k)*[-cos(k*t) - (-1)] = mu*(F/k)*[cos(k*t) - 1], not mu*(F/k)*cos(k*t).

 

[robcowlam]

Ah yes I see it now, I wasn't evaluating the integral, thanks for your help.