A load weighing 400 g vibrates with an amplitude of 15 cm on a spring with a stiffness of 25 N / m.

A load weighing 400 g vibrates with an amplitude of 15 cm on a spring with a stiffness of 25 N / m. Write the equation for the vibrations of the load.

1) Harmonic oscillations, i.e. such oscillations that are expressed by a sinusoidal function, arise when the restoring force is proportional to the displacement from the equilibrium position, but has the opposite sign:

F = – k * x.

2) For such a dependence, the offset x is expressed by the function:

x = x0 * sin (ωt), where

x0 – vibration amplitude,

ω is the angular frequency of the oscillation.

3) The angular frequency depends on the stiffness of the spring and the mass of the load as follows:

ω = √ (k / m) = √ (25 / 0.4) ≈ 7.9 (1 / s).

Therefore, we get the following equation for this oscillation:

x = 0.15 * sin (7.9t).