Pendulum Confusion

[Postictal Raiden]

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I know that based on the T = 2pi sqrt(L/g) the mass of the object doesn't affect the period of the pendulum. However, the equation of T = 2pi sqrt(m/k) suggests otherwise. How can I settle this dispute?

 

[Meredith92]

The second equation you listed only applies to springs I believe...

 

[Postictal Raiden]

The second equation you listed only applies to springs I believe...

I see. That makes sense. I should've realized that k in the second equation is the spring constant and that it doesn't apply to pendulums.

 

[milski]

Where is the dispute? These are two separate equations related to two separate systems. The first one is for pendulum (with small deviation from equilibrium), the second one is for a a mass on a spring. The harmonic motion in each of them is achieved in a different way.

 

[Postictal Raiden]

Where is the dispute? These are two separate equations related to two separate systems. The first one is for pendulum (with small deviation from equilibrium), the second one is for a a mass on a spring. The harmonic motion in each of them is achieved in a different way.

Yeah, I realized that after reading Meredith's response.

 

[sdm33]

I have a question if the pendulum using a spring and moving back and forth , can we consider the mass ?

 

[milski]

I have a question if the pendulum using a spring and moving back and forth , can we consider the mass ?

You mean if the pendulum is attached on a spring instead of string? The resulting motion will depend on the mass of the pendulum but will not be simple harmonic motion.

There are a lot of contraptions that you can make with springs and pendulums but you should not expect any of these on the MCAT.

 

[sdm33]

I hope not, By the way is that you house for sale on 98103 Troll Ave N Seattle, WA . lol

 

[sazerac]

I know that based on the T = 2pi sqrt(L/g) the mass of the object doesn't affect the period of the pendulum. However, the equation of T = 2pi sqrt(m/k) suggests otherwise. How can I settle this dispute?

Food for thought: in both equations the numerator (L or m) is the inertial component of the system - the larger it is the more the system will continue to move in the same direction. The denominator (g or k) is the restoration component of the system - the larger it is, the faster the system will switch directions and return to the neutral position and then zoom in the other direction.

This helped me learn / derive / remember these equations.

 

[Postictal Raiden]

Food for thought: in both equations the numerator (L or m) is the inertial component of the system - the larger it is the more the system will continue to move in the same direction. The denominator (g or k) is the restoration component of the system - the larger it is, the faster the system will switch directions and return to the neutral position and then zoom in the other direction.

This helped me learn / derive / remember these equations.

Wow. This is one of the most helpful tips I read on SDN. Thanks.