Please explain whether we use w d or w o in our equations for finding amplitude
ID: 2877245 • Letter: P
Question
Please explain whether we use wd or wo in our equations for finding amplitude and phase shift.
A body of mass 5 gr attached to a vertical spring stretches it 1000/9 cm to reach an equilibrium position. When the body moves in the air it experiences a resistance opposite to its movement, proportional to its speed. with a damping constant d = 50 gr/sec. Approximate the acceleration of gravity by g = 1000 cm/sec^2. Find the spring constant fc and the body-spring natural frequency w_0. Find a differential equation of the form y" = 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+ greaterthanorequalto if the roots are complex, then r plusorminus - alpha plusorminus beta, with alpha, beta reals and beta > 0 At t_0 = 0 sec the body is pulled down an additional 3 cm and then released with an initial velocity of 5 cm/sec. Find the solution y of the equation in part (b).Explanation / Answer
solution:
question:
Please explain whether we use wd or wo in our equations for finding amplitude and phase shift.
answer:
we will have to use wd in our equations as there is damping in the system so it must be considered and we cannot use free oscillation frequency i.e wo for finding the amplitude and phase shift