Question

An object with mass 0.160 kg is acted on by an elastic restoring force with force constant 11.0 N/m . The object is set into oscillation with an initial potential energy of 0.140 J and an initial kinetic energy of 7.00×10−2 J . What is the value of the phase angle ϕ if the initial velocity is positive and the initial displacement is negative?

Answer 1

Given
mass m= 0.160 kg
force constant =11.0
initial potential energy = 0.140 J
initial kinetic energy = 7.00×10−2 J .
The initial potential energy is 0.14 J = 2/3 of the total energy,
so the initial x^2 is 2/3 of A^2,
and x/A = sqrt(2/3),
cos^-1[sqrt(2/3)] = 35.26 degrees.
As the initial displacement is negative and the initial velocity positive, the object has just left its extreme negative position and must
go through 180-35.26 = 144.74 degrees to achieve its extreme positive displacement,

so the motion could be represented as
A cos(omega t - 144.74 degrees)
"phase angle" = 144.74 degrees