Find the equation of motion of a particle moving along the x axis if the potential energy is V = 1/2 kx2. (This is a simple harmonic oscillator

Consider the motion of a particle of mass m = 2 for x > 0, assuming it is subject to the following force: f = 4/x2 -1  Find the turning points and the period of the motion

A spring/mass/dashpot system has mass 5 kg, damping constant 70 kg/sec and spring constant 845 kg/sec/sec. Express the ODE for the system in the form a"+ 2px' + wr = 0 Identify the natural (undamped) frequency of the spring: wo 3= (square Hz) Identify the parameter p: (Hz) Now assume that the system has the oscillating forcing function cos(wod) with the same frequendy as the spring's natural frequency. + 14a'+ 169a = cos(wat) Find the general solution.

A simple harmonic oscillator is at equilibrium when the mass is at position x =0. The mass ispulled to x = +12 cm and released from rest.Rank the speed of the mass when it is at the following positions from least to greatest.