Question

A car bounces up and down on its springs at 1.0 Hz with only the driver in the car. Now the driver is joined by four friends. The new frequency of oscillation when the car bounces on its springs is

Answer 1

The new frequency of oscillation when the car bounces on its springs is 0.447 Hz

Frequency of oscillation of spring

The frequency of oscillation of the spring is given by f = (1/2π)√(k/m) where

• k = spring constant and
• m = mass on spring

Now since k is constant, and f ∝ 1/√m.

So, we have f₂/f₁ = √(m₁/m₂) where

• f₁ = initial frequency of spring = 1.0 Hz,
• m₁ = mass of driver,
• f₂ = final frequency of spring and
• m₂ = mass on spring when driver is joined by 4 friends = 5m₁

So, making f₂ subject of the formula, we have

f₂ = [√(m₁/m₂)]f₁

Substituting the values of the variables into the equation, we have

f₂ = [√(m₁/m₂)]f₁

f₂ = [√(m₁/5m₁)]1.0 Hz

f₂ = [√(1/5)]1.0 Hz

f₂ = 1.0 Hz/√5

f₂ = 1.0 Hz/2.236

f₂ = 0.447 Hz

So, the new frequency of oscillation when the car bounces on its springs is 0.447 Hz

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