College Algebra & Trigonometry

A weight is attached to an elastic spring that is suspended from a ceiling. If the weight is pulled 1 inch below its rest position and released its displacement in inches after t seconds is given by x(t)=2cos(5ðt+ð/3). Find the first two times for which the displacement s 1.5 inches.

1. 👍 0
2. 👎 0
3. 👁 95
1. what's the problem? You have the formula:

x(t) = 2cos(5pi t + pi/3)
just solve

2cos(5pi t + pi/3) = 3/2
cos(5pi t + pi/3) = 3/4

cos .722 = .75

so,
5pi t + pi/3 = .722 or 2pi-.722=5.560
t = (.722-pi/3)/5pi = -.021 or 6.262
t = (5.560-pi/3)/5pi = .287

see the graph at

http://www.wolframalpha.com/input/?i=solve+2cos%285pi+t+%2B+pi%2F3%29+%3D+3%2F2

You need to find the next occurrence after 0.287 by noting that the period is 0.4

1. 👍 0
2. 👎 0
posted by Steve

Similar Questions

1. College Algebra and Trigonometry

A weight is attached to an elastic spring that is suspended from a ceiling. If the weight s pulled 1 inch below its rest position and released its displacement in inches after t seconds is given by x(t)=(5pt+p/3. Find the first

2. College Algebra and Trigonometry

A weight is attached to an elastic spring that is suspended from a ceiling. If the weight s pulled 1 inch below its rest position and released its displacement in inches after t seconds is given by x(t)=(5pt+p/3. Find the first

3. Physics

Three different masses are attached to a spring which hangs down vertically from the ceiling. A metric ruler hangs from the ceiling next to the spring and measures how far from the ceiling the sping hangs. When a 110 N weight is

asked by Morgan on October 25, 2016
4. Math (PreCalculus)

A spring with a weight attached is oscillating. The weight (which is attached at the bottom of the spring) is 5 feet from a 10-foot ceiling when it’s at rest. The motion of the weight can be described by the equation:

asked by Steve on December 25, 2014
5. Physics

A 3.2 kg block is hanging stationary from the end of a vertical spring that is attached to the ceiling. The elastic potential energy of this spring/mass sytem is 2.2 J. What is the elastic potential energy of the system when the

asked by Mary on April 2, 2007
6. Physics

A vertical spring has one end attached to the ceiling and a 2.50 kg weight attached to the other one. When the system is at rest, the spring is stretched by 20.0 cm. Now let the weight drop from a position in which the spring is

asked by Timo on June 29, 2011
7. PHYSICS

A block weighs 15 N and is suspended from a spring that is attached to the ceiling. The spring stretches by 0.075 m from its unstrained length. By how much does the spring stretch when a 24-N block is suspended from it?

asked by Anonymous on November 4, 2015
8. Physics Urgent

A 3.2 kg block is hanging stationary from the end of a vertical spring that is attached to the ceiling. The elastic potential energy of this spring/mass sytem is 2.2 J. What is the elastic potential energy of the system when the

asked by Papito on April 24, 2007
9. Physics

An unstretched spring with spring constant 37 N/cm is suspended from the ceiling. A 3.3 kg mass is attached to the spring and let fall. To the nearest tenth of a centimeter, how far does it stretch the spring?

asked by Jay on September 24, 2013
10. physics

An object is attached to the lower end of a 100-coil spring that is hanging from the ceiling. The spring stretches by 0.210 m. The spring is then cut into two identical springs of 50 coils each. As the drawing shows, each spring

asked by jim on November 17, 2012

More Similar Questions