Can someone help with initial value problem, i will write it out

Question

anonymous · Answer

$$d^2s/dt^2=-16\cos(4t+\pi), s'(0)=400 and s(0)=0$$

anonymous · Answer

i know we are suppose to integrate both sides but i am getting lost

hero · Answer

Yeah, I'm not sure if I can help you much with this...What are you studying?

anonymous · Answer

its calc 2

hero · Answer

What section?

anonymous · Answer

evlautating defnite integrals

hero · Answer

Yeah, this is beyond me at the moment. I'd have to look it over

anonymous · Answer

can you pssible repost this and see if you can get me some help

hero · Answer

I can try to get the solution..

anonymous · Answer

but i want to know how to do it

hero · Answer

Yes, that's what I mean...I can try to get you the steps

anonymous · Answer

i have solved intial value problems but only ones where i was given first derivative only , but this one has the second derivative.  And i try and solve it but i am not getting the right answer

anonymous · Answer

if i integrate a second derivative, i should get the first derivative right? but would it have a +C at the end or no?

hero · Answer

across, help him

anonymous · Answer

you would have the +C after integration then u just plug in 0 for t and solve I think?

so d2s/dt2=−16cos(4t+π) , ds/dt = $$-16\sin(4t+\pi)/(4t+\pi)$$ + C
and since s'(0) = 400 = -16sin(4(0)+pi)/(4(0)+pi) +C .......so C= 400?? I dunno lol

anonymous · Answer

across solved it for me, thanks though guys