HELLO EVERYONE! THIS IS ONLY 1 QUESTION RELATED TO MECHANICAL PHYSICS, PHY254. PLEASE IF YOU CAN HELP BY SHOWING WUTH HANDWRITING AND NOT TYPED. I WOULD GLADLY APPRICIATE IT. THANK YOU SO MUCH FOR YOUR HELP! THE TEXTBOOKS ARE: Introduction to Classical Mechanics BY DAVID MORIN, Chaotic Dynamics, 2nd Edition BY Gregory L. Baker; Jerry P. Gollub, AND Vibrations and Waves BY A.P. FRENCH.

2 Revisiting undamped resonanceConsider an undamped simple oscillator consisting of a mass m and a spring k, driven by a force F 2 F0 costwt). 2.1. Consider the resonant case. i.e., w = am. In the lecture notes, we saw without justication that the solution for the position was 1 Jr x(t)=EAf-wgrcos[wnt], (1) with Af = Fol k the amplitude of the driving. Demonstrate that it is so. Hint: you don't need to guess a solution. Just plug it in a standard and relevant ODE, and conrm that this solution written above works. 2.2. We now drive the oscillator offresonance, with a force and m we. The power it is supplying to the oscillator is P = F u. Show that the average power supplied over one period. P. is zero