- #1
Spectre5
- 182
- 0
Hey
I was wondering if someone would check my work on this problem:
Note:
[tex]{\cal L}[/tex] = Laplace
[tex]{\cal U}[/tex] = Unit Step Function
[tex]{\cal L} \{ \cos(2t) \,\,\, {\cal U} (t - \pi)\}[/tex]
[tex]=e^{-\pi s} {\cal L} \{ \cos(2(t + \pi)) \}[/tex]
[tex]=e^{-\pi s} {\cal L} \{ \cos(2t + 2\pi) \}[/tex]
[tex]=e^{-\pi s} {\cal L} \{ \cos(2t) \}[/tex]
[tex]=\frac{se^{-\pi s}}{s^2+4}[/tex]
Can anyone help me with this problem:
[tex]{\cal L} \{ \sin(t) \,\,\, {\cal U} (t - \pi/2)\}[/tex]
[tex]=e^{-\frac{\pi s}{2}} {\cal L} \{ \sin(t + \pi / 2) \}[/tex]
[tex]=e^{-\frac{\pi s}{2}} {\cal L} \{ \cos(t) \}[/tex]
[tex]=\frac{s \, e^{-\frac{\pi s}{2}}}{s^2 + 1}[/tex]
But this is different from the books published answer (in the exponential, they do not have it divived by two, they just have e^(-pi*s)...but the rest of it the same...also the solution manual did the problem differently, it changed the sin(t) to cos(t - pi/2)...but then wouldn't that just convert back to sin(t)? Anyways...it skips a lot of work and just ends up with the answer after that step
I was wondering if someone would check my work on this problem:
Note:
[tex]{\cal L}[/tex] = Laplace
[tex]{\cal U}[/tex] = Unit Step Function
[tex]{\cal L} \{ \cos(2t) \,\,\, {\cal U} (t - \pi)\}[/tex]
[tex]=e^{-\pi s} {\cal L} \{ \cos(2(t + \pi)) \}[/tex]
[tex]=e^{-\pi s} {\cal L} \{ \cos(2t + 2\pi) \}[/tex]
[tex]=e^{-\pi s} {\cal L} \{ \cos(2t) \}[/tex]
[tex]=\frac{se^{-\pi s}}{s^2+4}[/tex]
Can anyone help me with this problem:
[tex]{\cal L} \{ \sin(t) \,\,\, {\cal U} (t - \pi/2)\}[/tex]
[tex]=e^{-\frac{\pi s}{2}} {\cal L} \{ \sin(t + \pi / 2) \}[/tex]
[tex]=e^{-\frac{\pi s}{2}} {\cal L} \{ \cos(t) \}[/tex]
[tex]=\frac{s \, e^{-\frac{\pi s}{2}}}{s^2 + 1}[/tex]
But this is different from the books published answer (in the exponential, they do not have it divived by two, they just have e^(-pi*s)...but the rest of it the same...also the solution manual did the problem differently, it changed the sin(t) to cos(t - pi/2)...but then wouldn't that just convert back to sin(t)? Anyways...it skips a lot of work and just ends up with the answer after that step
Last edited: