Question

A 4.8 kg block attached to a spring executes simple harmonic motion on a frictionless horizontal surface.The amplitude is 0.90 m, the maximum acceleration is 2.9 m/s^2. The force constant of the spring is closest to?

Answer 1

Let us pose x(t) = A sin (omega t + phi), with omega^2 = k/m, m = 4.8 kg, A = 0,9 m

dx/dt = A omega cos (omega t + phi)

dx^2/dt^2 = -A omega^2 sin(omega t + phi) => a_max = A omega^2 = A k / m => k =a_max m/ A = 15.5 N/m