Ratio for Kindetic and Potential energy

[Awer1]

If the phase angle for a block-spring system in SHM is φ and the block's position is given by x = xm cos(ωt+φ), what is the ratio of the kinetic energy to the potential energy at time t = 0? State your answers in terms of the given variables.



x =x_m Cos(wt + phi)
v = -w(x_m)sin(wt +phi)
K = (1/2 mv²)
P = (1/2 m w² x²)




dividing K/P = [v/wx]²
substitute v and x we get: [(-w(x_m)sin(wt +phi)/(w)(x_m Cos(wt + phi))]²
simplifying we get: [-wtan(wt + phi)/w]² = [tan(wt + phi)]²
at t = 0 we should get the following: [v/wx]² = [tan(phi)]²

The answer is marked wrong, am I interpreting the question incorrectly? I know what ratio is.. and ratio for Kinetic energy and Potential should be K/P right?

 

[thebigstar25]

you are absolutely right ! its odd that it is marked wrong .. maybe you should change the form of your answer? try different form maybe that will work ..

 

[Awer1]

oh good I thought I was going crazy. I was only allowed three attempts. so I used three different formats that were all the same thing.. still marked wrong.

 

[thebigstar25]

it happens, sometimes you have the right answer but i.e you have to express it in a certain form or in a certain sigificance .. :) anyway, don't worry you had the right answer ..