Question

CHALLENGE:
The equation of motion for a weight suspended from a particular spring is d( t)=5sin4t-2cos4t, where d is the displacement from the equilibrium position in centimetres and t is the time elapsed in seconds.
How many time does the weight pass through the equilibrium position in the first two cycles?

Answer 1

equation: \[d(t)=5\sin4t-2\cos4t\]

Answer 2

help meeeeeeeeeeee :'(

Answer 3

well you would have to solve for when d(t) = 0

--> 5sin(4t) = 2cos(4t)
Note: sin/cos = tan
--> tan(4t) = 2/5

--> 4t = arctan(2/5) = .3805
t = 0.095

Now 2 cycles means 2 periods, Period = 2pi/4 = pi/2, 2*pi/2 = pi
--> 0 < t < pi/4 or 0< t < .785

Answer 4

YES, this is the step that i was looking for.
I totally forgot about going from sin and cos to tan by division.

Thanks a lot for this!

Answer 5

so the final answer is 1 because t only equals 0.095 in range of 0<t<0.785?
just making sure.

Answer 6

yeah thats what i get :)

Answer 7

ok thanks!