Question

a 0.1 kg object oscillates as a simple harmonic motion along x axis with a frequency f=3.185 hz. At a position x1 , the object has a kinetic energy of o.7 j and a potential energy 0.3 J.The amplitude of oscillation A is:​

Answer 1

The total energy must be .7 J + .3 J = 1 J for a particle at the endpoint or midpoint of motion.

Also, omega = (k / m)^1/2

f = omega / (2 * pi)

omega^2 = 4 pi^2 * f^2 = k / m

k = 4 * pi^2 * f^2 * m = 40.05

Max KE or PE = 1/2 k A^2

A^2 = 2 * E / k = 2 * 1 / k = .0499

A = .223 meters