Proceed as in Examples 3 and 4 and use the given information

Proceed as in Examples 3 and 4 and use the given information to express the equation of simple harmonic motion y(t) = yo cos(Omega t + v_0/omega) sin(w t) for a spring/mass system in the trigonometric form y(t) = A sin(Omega t +). (Round your value for to four decimal m = 1/25 slug, y_0 = 1/2 ft, k = 1 lb/ft, and v_0 = 3/2 ft/s Give the amplitude, period, and frequency of motion.

Solution

m = 1/25

yo = 1/2 feet

k = 1

vo = 3/2

frequency = sqrt ( k/m ) = sqrt ( 1 / 1/25 ) = sqrt (25) = 5

frequency = 5 cycles/second

time period = 1/ f

f = w / 2pi

w = 5

f = 5 / 2pi = .7961

T = 1/ .7961 = 1.25 seconds

period = 1.25 seconds