Harmonic Motion 2: Sally & Mommy Ride the Least Exciting Carnival Ride

In summary, the world's least exciting carnival ride consists of a cloth sling suspended by a spring with a force constant of 225 N/m. Children sit in the sling and oscillate up and down slowly. Little Sally tries the ride and calls for help, but her mother reassures her and they ride together with a longer period of 3.32 seconds. Cletus the Carny uses this information to derive the mass of Sally's mother.
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phySicNewB
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The world's least exciting carnival ride consists of a cloth sling (of negligible mass) hanging by a spring of force constant k = 225 N/m. Children sit in the sling and bob up and down slowly. How exciting ...

Little Sally tries the ride. She gets into the sling, and, after Cletus the Carny gives her a bit of a push, oscillates up and down with a period of 1.78 seconds.

"Mommy, mommy, help, it's scary!" cries Sally. Her mother replies, "Don't worry, dear, you can sit on my lap and we'll ride together."

Together, Sally and her mother bob up and down with a period of 3.32 seconds.

Cletus scratches his head for a moment, then derives the mass of Sally's mother. What is it?
 
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What have you attempted so far? You must have some idea of how to approach the problem. If not, tell us what you don't understand.
 

What is harmonic motion?

Harmonic motion is a type of periodic motion in which an object moves back and forth around a central equilibrium point. It is characterized by a restoring force that is directly proportional to the displacement from the equilibrium point.

How is harmonic motion different from other types of motion?

Harmonic motion is different from other types of motion because it is periodic and follows a specific mathematical pattern. It also occurs when there is a restoring force acting on the object, such as gravity or a spring.

What is the purpose of studying harmonic motion?

Studying harmonic motion allows scientists to understand and predict the behavior of objects in motion. It is also important in fields such as engineering, where it is used to design and improve structures and machines.

What factors affect the frequency of harmonic motion?

The frequency of harmonic motion is affected by the mass of the object, the amplitude of the motion, and the strength of the restoring force. It is also influenced by external factors such as air resistance or friction.

How is harmonic motion used in real-life applications?

Harmonic motion is used in many real-life applications, such as pendulum clocks, musical instruments, and even roller coasters. It is also used in fields such as seismology to study earthquakes and in medicine to measure heartbeats and other biological rhythms.

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