Question

Here on Earth you hang a mass from a vertical spring and start it oscillating with amplitude 1.9 cm. You observe that it takes 3.0 s to make one round trip. You construct another vertical oscillator with a mass 6 times as heavy and a spring 10 times as stiff. You take it to a planet where gplanet = 8.8 N/kg. You start it oscillating with amplitude 4.8 cm. How long does it take for the mass to make one round trip?

Answer 1

T = 3.23 s

Step-by-step explanation:

In the simple harmonic movement of a spring with a mass the angular velocity is given by

w = √ K / m

With the initial data let's look for the ratio k / m

The angular velocity is related to the frequency and period

w = 2π f = 2π / T

2π / T = √ k / m

k₀ / m₀ = (2π / T)²

k₀ / m₀ = (2π / 3.0)²

k₀ / m₀ = 4.3865

The period on the new planet is

2π / T = √ k / m

T = 2π √ m / k

In this case the amounts are

m = 6 m₀

k = 10 k₀

We replace

T = 2π√6m₀ / 10k₀

T = 2π √6/10 √m₀ / k₀

T = 2π √ 0.6 √1 / 4.3865

T = 3.23 s