A weight is oscillating on the end of a spring see figure Th

tle Everything is an argument Botanya An Int. Fifth Edition Products l Jo. lett Learning MCAT CARS -h McAT Bog watch Movies. 2smovies to Pretorownan.orty Meath SARLARiowhed points Lartnga 23089. 2,3 Solving Trigonometric Eqwations A weight is oscillating on the end of a spring (see figure). The position of the weight relative tothe point of equabrium is given by y 12(oos Be- 7 sin 8t) where y is the displacement on and t is the time (n seconds). Find the times when the welight is at the paint of equilbrium (y- oy for osts 1. (Enter wour answers a domma-reparase list. Round your answers to two decimal places.) Equilibrium Submit Answer Save Progress Practice Another Version o 1n points Provious Answers La 2.3 504xP response in radians solve the multiple-angle equation. (Enter your answers as a comma separated list. Let n be any integar Enter vour 3 9 3 0141 points

Solution

We have given Y= 1/12 (cos 8t - 7 sin 8t) for 0<=t<=1

the times when the weight is at the point of equilibrium ( y =0) are the solutions to equation

1/12 (cos 8t - 7 sin 8t) =0

cos8t=7sin8t

by cross multiplication

1=7tan8t

tan8t=1/7

8t=arctan(1/7)=0.14189

8t=0.14189+k*pi radian

t=(0.1489/8)+k*(pi/8) where k is any integer

t=0.02+0.39k second since rounding to two decimal places

if 0<=t<=1,then the restrictions on k are

0<=0.0186+0.3926k<=1

-0.0186<=0.3926k<=1-0.0186

-0.0186<=0.3926k<=0.9814

(-0.0186/0.3926)<=k<=(0.9814/0.3926)

-0.04737<=k<=2.4997

k=0 or k=1 or k=2

the times when the weight is at the point of equilibrium are

t=0.02+0.39k

when k=0

t₀=0.02+0.39*0=0.02 s

when k=1

t₁=0.02+0.39*1=0.41 s

when k=2

t₂=0.02+0.39*2=0.8 s

t={0.02,0.41,0.8}