Question

An object of mass m is oscillating back and forth in simple harmonic motion. The maximum origin, x = 0, and moving in the x direction. Find the following in terms of m, T, and A:(a)The equation of motion of the object, (b)The maximum speed of the object (c)The maximum distance from equilibrium is A, and the period of oscillation is T. At t = 0 the object is at the acceleration of the object.(d)The total energy of the object.​

Answer 1

x = A sin ω t equation of motion

max speed = A ω

max distance (max value of x) = A

max KE = 1/2 m V^2 = 1/2 m A^2 ω^2

f (frequency) = ω / 2 π = 1 / T or T = 2 π / ω

ω = 2 π / T substitute for ω to put in terms of T