This is the missing equation that models the hieght and is misssing in the question:
h= 7cos(Ο/3 t)
Answers:
a. Solve the equation for t.
1) Start: h= 7cos(Ο/3 t)
2) Divide by 7: (h/7) = cos(Ο/3 t)
3) Inverse function: arc cos (h/7) = Ο/3 t
4) t = 3 arccos(h/7) / Ο β answer of part (a)
β¨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.
1) h = 1 cm β t = 3 arccos(1/7) / Ο
t = 1.36 sβ answer
2) h = 3 cm β t = 3arccos (3/7) / Ο =Β 1.08sβ answer
3) h = 5 cm β 3arccos (5/7) / Ο = 0.74 sβ answer
β¨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.
Use the periodicity property of the function.
The periodicity of cos(Ο/3 t) is 6.
So, the second times are:
1) h = 1 cm, t = 6 + 0.45 s = 6.45 s β answer
2) h = 3 cm β 6 + 1.08 s = 7.08 sβ answer
3) h = 5 cm β t = 6 + 0.74 s = 6.74 s β answer
