Hi Brombo,
That's a very nice result. I'll use it in my education!
Regarding your previous questions: The correct statement in Python/SymPy
should be:
solution = 2 *
sp.integrate(sp.re(solution_in_frequency_domain*sp.exp(sp.I*2*sp.pi*phi*t)),(phi,0,4))
I arbitrarily chose 4 as an cutoff value for the frequenciesbecause higher
values seem negligible. I only used the real part because the original
problem is the real-valued vibrations of a SDOF system fored by a block
function.
Op maandag 13 februari 2023 om 16:31:29 UTC+1 schreef brombo:
> I have tracked down the errors and the analytic and numerical results now
> agree (see attached) -
> On 2/10/23 11:32 AM, 'Tom van Woudenberg' via sympy wrote:
>
> This is the result in Python (same as in Maple): [image: downloaden
> (5).png]
>
> Op vrijdag 10 februari 2023 om 17:31:50 UTC+1 schreef Tom van Woudenberg:
>
>> Hi Brombo,
>>
>> Thank you for the update. It seems my previous posts didn't show up.
>> Anyway, you result doesn't match the result in Maple and the numerical
>> evalution of the integral in Python:
>>
>> Would be wonderful if we'd find an analytical solution.
>> Op vrijdag 10 februari 2023 om 01:08:56 UTC+1 schreef brombo:
>>
>>> Attached are latest results (I had calculated the roots of the quadratic
>>> wrong) and a plot -
>>> On 2/8/23 4:24 AM, 'Tom van Woudenberg' via sympy wrote:
>>>
>>> Hi Brombo,
>>>
>>> Thank you for the extensive working-out. I really appreciate that!
>>> However, the result doesn't seem to match the result in got in Maple
>>> (below result in Python for N(t):
>>>
>>> [image: Schermafbeelding 2023-02-08 094041.jpg]
>>> Do you have any ideas on the difference?
>>> Op woensdag 8 februari 2023 om 01:10:05 UTC+1 schreef brombo:
>>>
>>>> I didn't proof read well enough. Typo in equation 4. Correction
>>>> attached
>>>> On 2/7/23 3:02 AM, 'Tom van Woudenberg' via sympy wrote:
>>>>
>>>> Thank you brombo, I'll take a closer look at the file you send me!
>>>>
>>>> Op maandag 6 februari 2023 om 22:29:25 UTC+1 schreef brombo:
>>>>
>>>>> I cleaned things up here is what the notebook looks like (see attached
>>>>> html) -
>>>>>
>>>>>
>>>>> On 2/6/23 10:36 AM, 'Tom van Woudenberg' via sympy wrote:
>>>>>
>>>>> Hi there,
>>>>>
>>>>> When trying to solve a integral as part of a manual inverse fourier
>>>>> transform, SymPy return the unevaluated integral. Does anybody know if
>>>>> SymPy is able to solve this integral with some help? It would be good
>>>>> enough if I'd be able to obtain the result for specific values of t.
>>>>>
>>>>> import sympy as sp
>>>>> phi,t = sp.symbols('phi,t',real=True)
>>>>> sp.I*(1 -
>>>>> sp.exp(4*sp.I*sp.pi*phi))*sp.exp(-8*sp.I*sp.pi*phi)/(2*sp.pi*phi*(-4*sp.pi**2*phi**2
>>>>>
>>>>> + 1.5*sp.I*sp.pi*phi + 4))
>>>>> solution_numeric = 1 / sp.pi * sp.integrate(sp.re
>>>>> (solution_in_frequency_domain_numeric*sp.exp(sp.I*2*phi*t)),(phi,0,4))
>>>>> print(solution_numeric)
>>>>>
>>>>> returns:
>>>>> (Integral(sin(4*pi*phi)*re(exp(2*I*phi*t)/(-4*pi**2*phi**2*exp(8*I*pi*phi)
>>>>>
>>>>> + 1.5*I*pi*phi*exp(8*I*pi*phi) + 4*exp(8*I*pi*phi))), (phi, 0, 4)) +
>>>>> Integral(cos(4*pi*phi)*im(exp(2*I*phi*t)/(-4*pi**2*phi**2*exp(8*I*pi*phi)
>>>>> +
>>>>> 1.5*I*pi*phi*exp(8*I*pi*phi) + 4*exp(8*I*pi*phi))), (phi, 0, 4)) +
>>>>> Integral(-im(exp(2*I*phi*t)/(-4*pi**2*phi**2*exp(8*I*pi*phi) +
>>>>> 1.5*I*pi*phi*exp(8*I*pi*phi) + 4*exp(8*I*pi*phi))), (phi, 0,
>>>>> 4)))/(2*pi**2*phi)
>>>>>
>>>>> Plotting the result for t,0,15 should give this result according to
>>>>> Maple:
>>>>> [image: Schermafbeelding 2023-02-06 163521.jpg]
>>>>>
>>>>> Kind regards,
>>>>> Tom van Woudenberg
>>>>> Delft University of Technology
>>>>>
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