Introduction to Classical Mechanics · Problem 4.22
Conservation of energy and momentum — Morin
Physics — Mechanics · simple-harmonic-motion
Problem
A projectile of mass m is fired from the origin at speed v0 and angle θ. It is attached to the origin by a spring with spring constant k and relaxed length zero.
(a) Find x(t) and y(t).
(b) Show that for small ω≡k/m, the trajectory reduces to normal projectile motion. And show that for large ω, the trajectory reduces to simple harmonic motion, that is, oscillatory motion along a line (at least before the projectile smashes back into the ground). What are the more meaningful statements that should replace ``small ω'' and ``large ω''?
(c) What value should ω take so that the projectile hits the ground when it is moving straight downward?