The springs of a 1700-kg car compress 5.0 mm when its 66-kg driver gets into the driver seat. If the car goes over a bump, what will be the frequency of oscillations?

The  frequency of oscillations is 7 Hz

Explanation:

Given;

mass of car, = 1700 kg

mass of driver, = 66 kg

compression of the spring, x = 5mm = 0.005 m

The frequency of the oscillation is given as;

where;

k is force constant

m is the total mass of the car and the driver

m = 1700 kg + 66 kg = 1766 kg

Weight of the car and the driver;

W = mg

W = 1766 x 9.8

W = 17306.8 N

Apply hook's law, to determine the force constant;

F = kx

W = F

Thus, k = W/x

k = 17306.8 / 0.005

k = 3461360 N/m

Now, calculate the frequency

Therefore, the  frequency of oscillations is 7 Hz

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explanation:

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