At what time is the kinetic energy twice the potential energy first time?
The motion of a particle is given by x(t) = (25cm) cos(12t), where t is in s.
At what time is the kinetic energy twice the potential energy first time?
PE = (1/2) kx^2
KE = (1/2) kA^2 – (1/2)kx^2
KE = 2PE
=> (1/2) kA^2 – (1/2)kx^2 = 2 * (1/2) kx^2
=> A^2 = 3x^2
=> (25)^2 = 3 * [(25cm) cos(12t)]^2
=> cos^2 12t = 1/3
=> cos 12t = 1/√3
=> 12t = 0.9553
=> t = 0.08 s.
What is the first time at which the kinetic energy is twice the potential energy?