How this sin^2 changes to cos^2 ? Please help me .This is from the chapter of simple harmonic motion

Here, sin^2 doesn’t changes to cos^2 term but the enrgy is written in one other form.

As the eqn. of the SHM is:

x = Asin(wt + phi)

v = dx/dt = Awcos(wt + phi)

ANd the eeergy is also given as=> 0.5mv^2.

Hence putting the v value in it U would get ,

E = 0.5mA^2w^2cos^2(wt + phi) J

 

Hi Ahmed,

The first one is the kinetic energy! and the second one is the potential energy, hence the formulae are differrent!

remember- the kinetic energy depends on the velocity and it should be max at mean position while the potential energy depends on the position (here distance from the mean position) and it should be max at extremum position 

if you want derivations ask me further :)