Initial Angle of Pendulum: Solving for Angle Using SHM Equation

In summary, the initial angle for a pendulum with an angle given by (.10 rad)cos(5t + pi) where t is in sec is θ(0) = θmax * cos (phase constant). The phase constant is chosen such that the initial conditions, i.e. the angle at t=0, is satisfied. The initial angle is not the same as the phase constant, which is just a way to fix the values of the function at time t=0.
  • #1
bcjochim07
374
0

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.
 
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  • #2
bcjochim07 said:
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 :approve:. The initial conditions is simply a set of conditions which fix the values of a function at time t=0.
 
  • #3
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
 
  • #4
bcjochim07 said:
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?
 
  • #5
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?
 
  • #6
Hi bcjochim07! :smile:

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). :smile:
 

1. What is the equation for the initial angle of a pendulum?

The equation for the initial angle of a pendulum is θ0 = arcsin(A/E), where θ0 is the initial angle, A is the amplitude of the pendulum's swing, and E is the energy of the pendulum.

2. How does the initial angle affect the motion of a pendulum?

The initial angle of a pendulum determines the amplitude and period of its swing. A larger initial angle will result in a larger amplitude and longer period, while a smaller initial angle will result in a smaller amplitude and shorter period.

3. Can the initial angle of a pendulum be negative?

Yes, the initial angle of a pendulum can be negative. This means that the pendulum starts its swing from a position below the equilibrium point. However, when using the SHM equation to solve for the angle, the result will always be positive.

4. Is the initial angle of a pendulum affected by its mass?

No, the initial angle of a pendulum is not affected by its mass. The only factors that affect the initial angle are the amplitude and energy of the pendulum.

5. How is the initial angle of a pendulum measured?

The initial angle of a pendulum can be measured by using a protractor or a level. The pendulum should be at rest, with the string hanging straight down, and the angle can then be measured from the vertical line.

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