System A consists of a mass m attached to a spring with a force constant k; system B has a mass 2m attached to a spring with a force constant k; system C has a mass 3m attached to a spring with a force constant 6k; and system D has a mass m attached to a spring with a force constant 4k. Rank these systems in order of decreasing period of oscillation.

    T₂ > T₁ > T₃ >T₄

Explanation:

In a simple harmonic motion the angular velocity is

         w =

angular velocity and period are related

         w = 2π / T

we substitute

         T =

let's find the period for each case

a) mass m

   spring constant k

          T₁ = 2π

b) mass 2m

   spring constant k

          T₂ = 2π

          T₂ = T₁ √2

          T₂ = T₁ 1.41

c) masses 3m

   spring constant 6k

          T₃ = 2π

          T₃ = 2π

          T₃ = T₁ 0.707

d) mass m

    spring constant 4k

          T₄ = 2π

          T₄ = 2π

          T₄ = T₁ 0.5

now let's order the periods in decreasing order

           T₂ > T₁ > T₃ >T₄

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2