help me how to find the phi A body of mass 2 gr attached to a vertical spring st
ID: 1424308 • Letter: H
Question
help me how to find the phi
A body of mass 2 gr attached to a vertical spring stretches it 40 cm to reach the equilibrium position. Approximate the acceleration of gravity by g = 1000 cm/sec^2, and neglect any air resistance. Find the spring constant k and the body-spring natural frequency w_0. Find a differential equation of the form" = F(y, y') for the displacement function y from the equilibrium position, with y positive downwards. Use yp to denote de derivative y'. Find, r+, r-, roots of the characteristic polynomial of the differential equation in part (b). Convention: If the roots are real, then r+ greater than or equal to r_; if the roots are complex, then r plus or miniz e = alpha beta i, with alpha, beta reals and beta > 0. At t_0 = 0 sec the body is pushed up an additional 2 cm and then released with an initial velocity of -10 (3^-1/2) cm/sec. Find the solution y of the equation in part (b), and also provide the amplitude ^4 and the phase-shift pi in the interval (-pi, pi].Explanation / Answer
Idon't know if i undestrand corectly the request, anyway your solution is a linear combinantion of a sine term and a cosine one. Both terms depend upon the same time function, Thus theri realtive phase shift is 90°
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