angular speed in a harmonic motion

Question

Fig shows amass attached to two springs. The mass moves along a horizontal tube with one spring stretched and the other compressed. A narrow marked on the mass indicates its position on a scale. Fig1 shows the situation when mass is displaced through a distance x from its equilibrium position. The mass is experiencing an acceleration a in the direction shown. Fig2 shows a graph of the magnitude of the acceleration against the displacement x.

The mass-spring system of fig 1 can be used as a device to measure acceleration, called an accelerometer. It is mounted on a rotating test rig, used to simulate large g-forces or astronauts. Fig 3 shows the plan view of a long beam rotating about its axis A with the astronaut seated at end B, acing towards A. The accelerometer is parallel to the beam and is fixed under the seat 10m rom A

Fig-1

Fig-2

Fig- 3                    

When the astronaut is rotating at a constant speed, the arrow marked on the mass has a constant deflection. Explain why

Summary : angular speed in a harmonic motion due to mass