An object is oscillating at the end of a spring its

Question

Question: An object is oscillating at the end of a spring. Its position, in centimeters, relative to a fixed point, is given as a function of time, t, in seconds, by

y = y₀ cos(2Πωt), with ω a constant

(a) Find an expression for the velocity and acceleration of the object.

(b) How do the amplitudes of the position, velocity, and acceleration functions compare? How do the periods of these functions compare?

(c) Show that the function y satisfies the differential equation

(d²y/dt²) + 4Π²ω²y = 0