(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given the equation mx''+cx=cAsin(Ωt) with the initial conditions x(0)=0 and x'(0)=0.

Solve the initial value problem for the case when Ω < ω and show that |x(t)| < H provided

A < H(1-(Ω/ω)).

2. Relevant equations

3. The attempt at a solution

For my solution to the equation I got x(t)=(Aω/(ω^2-Ω^2))[ωsin(Ωt)-Ωsin(ωt)]

So, I'm hoping that this is right which I found using x(t)=x_h+x_p.

But I'm completely confused about the second part to show that |x(t)| < H provided

A < H(1-(Ω/ω)).

This is my first post here, so apologies if I'm not doing it right. :shy:

Thanks in advance.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# IVP applications of second-order ODE

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