Question

A horizontal mass spring oscillator is constructed, where the mass of the oscillator is 3 kg, the spring constant is 3 kg/s, and the friction parameter of the medium b kg/s. Denote the displacement of the oscillator from the equilibrium position by y(t).

Find the equation _______=0

The spring is critically damped when b=___

When b=0, the frequency of the oscillation will be ___s^-1. When b=3, the frequency of oscillation will be ____s^-1.

Answer 1

We know in general that the

Spring force F=-kx

Damping force f=-bv=-bx'

So the total forces acting on the system is

b=1 for critically damped

When b=0 then the frequency is given by

f=0.1591549430918 s^-1

When b=3 then

f=0.1378322238554 s^-1

By using the equation