The motion of a particle connected to a spring is described by x = 2 sin (4π t). At what time (in s) is the potential energy equal to the kinetic energy?

A.) 0.03
B.) 0.06
C.) 0.08
D.) 0.04
E.) 0.13

Question

The motion of a particle connected to a spring is described by x = 2 sin (4π t). At what time (in s) is the potential energy equal to the kinetic energy?

A.) 0.03
B.) 0.06
C.) 0.08
D.) 0.04
E.) 0.13

sidsiddhartha · Answer

0.04

sidsiddhartha · Answer

because sin4pi t=1/2

praxer · Answer

I think it is 0.06 second cause if the potential energy curve is following a cosine transition than the KE will follow a sine transition or vice verse so the term 4pi t = pi/4 t=1/16=0.0625 Siddhartha you made a wrong in assuming sin4pi t=1/2 it should be 1/root2 http://image.mathcaptain.com/cms/images/41/double-angle-formula-for-cosine.jpg see it once...:) @EducateMe understood.

praxer · Answer

this is the graphical relation between potential energy and kinetic energy.