Answer to Question #94849 in Trigonometry for may

Question

A mass suspended on a spring will exhibit sinusoidal motion when it moves. If the mass on a spring is 85 cm off the ground at its highest position and 41 cm off the ground at its lowest position and takes 3.0 s to go from the top to the bottom and back again, determine an equation to model the data.

Answer 1

$A$ - amplitude - the maximum displacement from the state of equilibrium:

$$A=\frac{0.85-0.41}{2}=0.22\text{ m}.$$

$\omega$ - angular frequency:

$$\omega=\frac{2\pi}{T}=\frac{2\cdot3.14}{3}=2.09\text{ s}^{-1}.$$

The equation of sinusoidal oscillations:

$$x(t)=A\space\text{sin}(\omega t)=0.22\space\text{sin}(2.09t)\text{ m}.$$