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anonymous
 4 years ago
CHALLENGE:
The equation of motion for a weight suspended from a particular spring is d( t)=5sin4t2cos4t, 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?
anonymous
 4 years ago
CHALLENGE: The equation of motion for a weight suspended from a particular spring is d( t)=5sin4t2cos4t, 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?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0equation: \[d(t)=5\sin4t2\cos4t\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0help meeeeeeeeeeee :'(

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.1well 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0YES, 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!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so the final answer is 1 because t only equals 0.095 in range of 0<t<0.785? just making sure.

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.1yeah thats what i get :)
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