A mass of 240 g oscillates on a horizontal frictionless surface at a frequency of 3.0 Hz and with amplitude of 4.5 cm.
a) What is the effective spring constant for this motion?
b) How much energy is involved in this motion
m = 240 g = 0.24 kg
A = 4.5 cm = 0.045 m
f = 3.0 Hz
g = 9.8 m/s^2
k= F/x = mg/x
E = K + U
K = 1/2*m*v^2
U = 1/2*k*x^2
v = ±ε√(A^2-x^2)
ε = 2πf = √(k/m)
v=0 when x=±A since the object stops briefly before travelling back towards the equilibrium.
^^^ That means K=0
The Attempt at a Solution
a) k= F/x = mg/x = [(0.240 kg)(9.8 m/s^2)]/(0.045 m) ≈ 52.27 N/m
b) E = 1/2*(52.27 N/m)(.045m)^2 = 0.053 J
^^^ Does this all look correct?