Pendulum Equation

This forum made possible through the generous support of SDN members, donors, and sponsors. Thank you.

MedPR

Membership Revoked
Removed
10+ Year Member
Joined
Dec 1, 2011
Messages
18,577
Reaction score
57
So TBR kind of sneaks this equation in and doesn't say a single thing about it. It's equation 5.10 if you have the 2011 book.

Theta=Thetamax(cos2pi)(frequency)(time)

When is the equation useful? And if you don't know theta, how do you know thetamax?
 
Last edited:
Are you sure you have it right? I would expect that the cosine is from everything after, so:
Theta=Thetamax * cos(2pi * frequency *time)

And you use it to find one of the unknows from the rest of them. As in when is the pendulum going to be at max deflection, given frequency and similar things.
 
Are you sure you have it right? I would expect that the cosine is from everything after, so:
Theta=Thetamax * cos(2pi * frequency *time)

And you use it to find one of the unknows from the rest of them. As in when is the pendulum going to be at max deflection, given frequency and similar things.


Oh, I don't know. I added in the parentheses to make it easier to read.

It actually says Theta = thetamaxcos2pifrequencytime
 
Oh, I don't know. I added in the parentheses to make it easier to read.

It actually says Theta = thetamaxcos2pifrequencytime

Yes, it's cos of the product of everything after the cosine, as I have it above. It describes the motion of a pendulum as a simple harmonic motion, relies on approximating sin(theta)=theta, which means that it's correct only for small theta. But you can assume small enough theta for all intro physics problems.

tl;dr: don't worry too much about it, just plug values as necessary when you have a problem which has them.
 
So the theta in that equation is referring to the arclength in radians, and not the angle between L and T or mg and mgcostheta?
 
So the theta in that equation is referring to the arclength in radians, and not the angle between L and T or mg and mgcostheta?

It's either - it is the same dimension as thetaMax. The formula is derived for the angle but if you multiply both sides with L (length of the string, radius), you'll get the arc length.

In other words: either theta and thetamax are both angles, or theta and thetamax are both arclengths.

The note that I made about sin(theta)=theta is related to the fact that the formula is only approximate. So it is fairly good approximation for theta being 1,2,5,10 degrees but gets worse and worse for pendulums swinging further up.
 
Top