Question

An object stretches a spring 6 inches in equilibrium. Find its displacement y for t> 0 (where y is the displacement of the object from its equilibrium position, measured positive upward), if it's initially displaced 3 inches above equilibrium and given a downward velocity of 6 inches/s. Find the frequency, period, amplitude and phase angle of the motion.

Answer 1

The block is balanced by 6 inches. Then K x = m g ; k/m can be calculated. From which angular frequency, frequency and time period will be obtained.

The displacement y = (3.01 inch) sin ( 8.02 t + 94.67o)

Femeie felel و دورو موقف V=whA²x² 6= A - 32 on squaring & albinls 36=2 / (4-9) rest in kXoang 216 + 9 = 4² 9 = 9.8m/p2 = 386 inlar In shore wash 216 +9 = A A=19.56 3 in 386 x=6 inch w=1386 0.56 +9=A2 = 3.01 in X= A sin(a+ht) At t=0 3=3.01 sind [28.02 nadly Sind= 2 20 8=85.330 1 f = 1.276 Hz A=3.01 inch LT=0.784 2 phase Constant d = 180-4, 70- 94.670 y=13.01 inch) sin 18.02t+94.67)