I am having problems solving for the amplitude for the damped part of the problem (c = 500).
The book gives a direct equation for this amplitude on p. 623 (eqn. 8/20). Is it acceptable to go straight to this equation?
If not, when you assume a solution of x = X_1*cos(omega*t) + X_2*sin(omega*t), both X_1 and X_2 will be nonzero. How do I find a single amplitude using both X_1 and X_2?
If you assume a solution of x = X*sin(omega*t - phi), I get stuck when plugging x, x_dot, and x_dot_dot back into the EoM. The left side of the equation has coefficients of cos*(omega*t - phi) and sin*(omega*t - phi) while the right side is simply F_0*cos(omega*t). How do I equate coefficients to solve for X?
4 comments:
All you need to do is use the equation we saw in the problem solving class to solve for X.
it is formula 8/20 on page 623.
It also follows sample problem 8/6 on page 628.
My question is what are you using for Fo? Are you assuming t = 0?
i assumed that t was 0 and ended up with a plausible answer
It is OK to use the equation for damped response on page 623. F0 for this problem is 1000 N.
For the undamped case, it is good practice to derive the result.
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