Simple Harmonic Oscillator - Critically Damped

[Muskkan]

Can someone answer this:

A critically damped simple harmonic oscillator starts from an amplitude of 5.0 cm and comes to rest at equilibrium 3.5 sec later. The simple harmonic oscillator is made of a .58 kg mass hanging from a spring with spring constant 150 N/m. Assuming the friction force is in the vertical direction, how big is the friction force?

[FizziksGuy]

Hi Muskkan.  Damped oscillators are outside the scope of AP Physics 1/2, but happy to help if I can.  How far have you gotten so far / where are you getting stuck?

[Muskkan]

Well, in AP Physics class we are using Giancoli 6th edition book. It doesn't have equations for Damped simple harmonic oscillator. I looked at the following link: http://farside.ph.utexas.edu/teaching/336k/lectures/node19.html but I do not know how to get started.

The given are Amplitude = .05 m, Time = 3.5 sec, Mass = .58kgs, k = 150 N/m and we nee to find Friction force.

[FizziksGuy]

I might start with a resource like this: https://opentextbc.ca/physicstestbook2/chapter/damped-harmonic-motion/ or this: https://www.toppr.com/guides/physics/oscillations/damped-simple-harmonic-motion/