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 Quote by sophiecentaur I already told you that all angles should be in radians - or you keep getting 2pi all over the place. For a start - your derivative is only correct if ω is in radians. Look up differentiating trig functions - basics of. Degrees suck in Science. Radians will be used all over the Universe (literally) by any civilisation with Maths but degrees are totally arbitrary.
I understand that the argument of a trigonometric function needs to be in radians (because the derivative of sinθ is only cosθ when θ is in radians), but what if it's outside the argument as it is in the equation of simple harmonic motion for a simple pendulum?

$$θ(t)={ θ }_{ max }cos(ωt+ϕ)$$

 Quote by sophiecentaur I don't know what those equations mean as you didn't define the variables so it is not possible to derive them. The "w" on the left hand side is not omega! And what is the theta? Is this describing a tortional vibration? Those angles aren't the same angles as the angular velocity in the vibration cycle. See how confusing it is when the variables aren't defined.
Opps, the "w" should've been omega. I took the derivative of the equation of simple harmonic motion for a simple pendulum. θ is the angle between the vertical line pointing towards the ground and the string of the pendulum.

 Quote by WannabeNewton I would like you to derive it yourself. It is very simple; just use the fact that this system conserves the total energy and that, by definition, ω2 = k / m.
I accept the challenge.

 Quote by WannabeNewton As for the second question, you are confusing the angular frequency of the period of the motion with the angular velocity of the mass. It is unfortunate that both have the same symbol for the particular case you are working with but use $\dot{\theta }$ instead for the angular velocity.
Oh. That's quite confusing to the novice. Makes sense now.