How Does the Phase Angle in SHM Equations Affect Displacement and Energy?

[sapiental]

question 1)

If a simple harmonic oscillation is described by the function

x = A sin (wt + phi)

would phi be the opposite of what it would be for a SHM described by the function

x = A cos (wt + phi)

I.e if the graph for for x = A sin (wt + phi) , when t = 0, x = +A. would phi be equal to pi instead of 0( as it would for x = A cos (wt + phi)question 2)

For a mass m attached to a spring that undergoes simple harmonic motion, The spring
constant is k.

Does the elastic potential energy ever equal the kinetic energy at one point x?

this isn't a homework question, just my curiosity..

Thanks

 

[courtrigrad]

1. If $$x = A\sin(\omega t + \phi)$$ and $$x = +A$$ at $$t = 0$$, then $$A = A\sin(\phi)$$.

So $$\phi = \frac{\pi}{2}$$

 

[sapiental]

thanks a lot!