The equation models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretched and then released.

Question

h=7 cos (pi/3 t)

a. Solve the equation for t.

b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.

c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time. Round your answers to the nearest hundredth.

Answer 1

(a)

 

h(t) = 7 cos(πt/3) ⇒

 

t = (3/π) cos^-1(h/7)

 

For parts (b) and (c), keep in mind that cos^-1(h/7) is multivalued.

 

(b)

 

Plug in h = +1, +3, and +5 cm and evaluate t at those positions.  Select the lowest positive value of cos^-1(h/7), i.e. positive minimum time, which corresponds to the first time at 1, 3, and 5 cm.

 

(c)

 

Plug in h = -1, -3, and -5 cm and evaluate t at those positions.  Select the next higher positive value of cos^-1(h/7), i.e. the second time at -1, -3, and -5.