Questopn about phase shift SHM

[Saladsamurai]

Question about phase shift SHM

The displacement of an object is given by
$$x(t)=x_mcos(\omega t+\phi)$$
If the inital displacement is 0 and the initial v is in the negative x direction, then the phase constant must be ___rads

I know that if x=o then the cosine of the phase must be 0
$$\cos(\omega t+\phi)=0$$

so$$\omega t+\phi=\frac{\pi}{2}$$

and I am stuck from here...hints?

 

[Dick]

Initial means t=0. So x(0)=xm*cos(phi). phi=pi/2 works for that. Is v(0) negative? If so then you have a solution.

 

[Saladsamurai]

Initial means t=0. So x(0)=xm*cos(phi). phi=pi/2 works for that. Is v(0) negative? If so then you have a solution.

v is in -x direction...that is where I am most confused, does that just mean that phi has to be negative?

 

[Dick]

It means v=dx/dt is negative at t=0.

 

[Saladsamurai]

It means v=dx/dt is negative at t=0.

Okay...
so if $$v=-\omega x_m\sin(\omega t+\phi)=-$$
and x_m=+
t=0
then $$-\omega x_m\sin(\phi)$$ is negative
so sin(phi) is positive
Thus, phi=+pi/2

Does that check out?

 

[Dick]

Looks ok to me. Draw a graph of cos(x) if you don't believe me.

 

[Saladsamurai]

Looks ok to me. Draw a graph of cos(x) if you don't believe me.

I will...cause I don't.
























No I won't...cause I do.
but I probably should so I can see the relationships...

Thanks again Dick.