A spring-mounted chair in which the astronaut sits, can be used to find the mass of an astronaut. The chair is then made to oscillate in simple harmonic motion. The spring used in one such device has a spring constant of 569 N/m, and the mass of the chair is 11 kg. The measured oscillation period is 3.6 s. Find the mass of the astronaut.

M = 175 kg

Explanation:

In the resolution of the harmonic oscillator movement of a system and a mass with a spring, the angular velocity is

w = √ k / m

Where k is the spring constant and m the mass

In this case the mass is the mass of the chair (m) plus the mass of the astronaut (M)

M all = m + M

The angular velocity and the period are related by

w = 2π / T

Substituting

2π / T = √ (k / (m + M))

We calculate the astronaut's mass

4π² / T² = k / (m + M)

M = k T² / 4π² - m

M = 569 3.6² / (4π²) - 11

M = 186.8 - 11

M = 175 kg