How To Find Initial Angular Velocity

[rockerdude1210]

Homework Statement

The angle of a pendulum is θ(t)=(0.270rad)cos(4.00t+1.00π), where t is in seconds.
Determine the initial angular velocity.

Homework Equations

ω=2πf

The Attempt at a Solution

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I solved for the frequency, which was 6.37E-1 Hz and subbed it into the formula above and got 4rad/s which is the same ω in the equation but it is wrong. Am I missing something because I can't figure out what is wrong with my method.

 

[andrewkirk]

The formula ω=2πf is not applicable to this case. That formula is for uniform circular motion, which has constant angular velocity, not for a pendulum, which has variable angular velocity.

From the formula for θ you can deduce that initially (at time t=0) the pendulum is at its highest point, and hence at zero angular velocity.

 

[rockerdude1210]

Ah okay, thanks!

Did you just sub in 0 for t which gave you -0.270 at the θ to figure out that it was at its highest point?

 

[andrewkirk]

Essentially yes. Cos attains its maximum absolute value at integer multiples of pi.

 

[rockerdude1210]

Makes sense, thank you!