Initial Angle of Pendulum: Solving for Angle Using SHM Equation

[bcjochim07]

Homework Statement

A pendulum's angle is given by (.10 rad)cos(5t + pi)
where t is in sec. What is the initial angle?

Homework Equations

The Attempt at a Solution

Do I plug in t= 0 to get this angle, or is the phase constant this angle? I read that the phase constant specifies initial conditions, but I'm not entirely clear on what it means.

 

[Hootenanny]

Do I plug in t= 0 to get this angle, or is the phase constant this angle? I read that the phase constant specifies initial conditions, but I'm not entirely clear on what it means.

Sounds good to me . The initial conditions is simply a set of conditions which fix the values of a function at time t=0.

 

[bcjochim07]

According to the equation above pi is my phase constant, but if I plug in t=0, I don't come up with pi as initial angle, so I'm not sure if phase constant and initial angle are the same thing

 

[Hootenanny]

so I'm not sure if phase constant and initial angle are the same thing

They're not, the phase angle is chosen such that the initial conditions, i.e. the angle at t=0, is satisfied. Does that make sense?

 

[bcjochim07]

I still don't understand. Could you describe it to me using the equation Theta(t) = theta max * cos (omega*t+ phase constant) with the values in the equation in the problem up above?

 

[tiny-tim]

Hi bcjochim07!

You're confused because, in this case, the amplitude is an angle, just like the phase constant.

Usually, the amplitude is a number or a length or a speed, so there's no confusion … the question would ask for the initial value, or the initial distance, or the initial speed … and you couldn't get that confused with the phase constant!

The initial angle is θ(0), which is θmax * cos (phase constant).