# Simple Harmonic Motion equation question: which length and why

• agenttiny200
In summary, the conversation discusses a physics question about finding the gravity on Planet X using a spring and a mass. The question asks why the amplitude of the oscillation is 28.2 cm instead of 10.4 cm. The solution is found by using the formula a=(2πf)2A and finding the spring constant. The conversation also touches on using differential equations and the formula g=(k×ΔL)/m to find the spring constant.
agenttiny200

## Homework Statement

I solved this physics question, but I am unclear about why Amplitude was the amount the spring was stretched by (which should be the new equilibrium point), instead of the amount the person pulled the mass down by (which should be the amplitude). Can anyone help?

On your first trip to Planet X you happen to take along a 300g mass, a 40-cm-long spring, a meter stick, and a stopwatch. You're curious about the acceleration due to gravity on Planet X, where ordinary tasks seem easier than on earth, but you can't find this information in your Visitor's Guide. One night you suspend the spring from the ceiling in your room and hang the mass from it. You find that the mass stretches the spring by 28.2cm. You then pull the mass down 10.4cm and release it. With the stopwatch you find that 10.0 oscillations take 16.7s. What is the gravity of Planet X?

a=(2πf)2A

## The Attempt at a Solution

f (frequency) =(10 oscillations/16.7s)= 0.5988 Hz
m (mass) =0.3 Kg
A (amplitude) = why 28.2 cm (0.282 m) instead of 10.4 cm (0.104 m)?

a=(2π×0.5988Hz)2×0.282m
a=3.99m/s2

You seem to be confusing the maximum acceleration of the mass, (2πf)2A, with the local gravitational acceleration.
Use the resting stretch information to find the spring constant. What differential equation do you get for the oscillation?

To find spring constant, there is k = (2πf)2m = 4.25. Not sure what you meant by differential equations, they gave us the number of oscillations (10) per 16.7s in the question. Its supposed to be a simple harmonic question.

Am I supposed to be using the formula g=(k×ΔL)/m? Isn't that for pendulums and not springs?

agenttiny200 said:
To find spring constant, there is k = (2πf)2m = 4.25.
Sure, but can you also express it in terms of the local gravity and the original extension?

g = (2πf)2 because (g/x) = (k/m) and (k/m) = (2πf)2 ?

agenttiny200 said:
g = (2πf)2 because (g/x) = (k/m) and (k/m) = (2πf)2 ?
Right reasoning, but I think you omitted something in g = (2πf)2

## 1. Why is the length of the pendulum important in the Simple Harmonic Motion equation?

The length of the pendulum is important because it determines the period of the oscillation, or how long it takes for the pendulum to complete one full swing. This period is used in the Simple Harmonic Motion equation to calculate the frequency and other important factors.

## 2. How do you determine the best length for a pendulum in Simple Harmonic Motion?

The best length for a pendulum in Simple Harmonic Motion can be determined by experimenting with different lengths and recording the period of oscillation for each length. The length that results in the most consistent and accurate period is considered the best length.

## 3. Can the length of the pendulum affect the amplitude of the oscillation?

No, the length of the pendulum does not affect the amplitude of the oscillation in Simple Harmonic Motion. The amplitude is determined by the initial displacement of the pendulum and the force of gravity.

## 4. Why is the Simple Harmonic Motion equation important in physics?

The Simple Harmonic Motion equation is important in physics because it helps us understand and predict the behavior of objects in oscillatory motion. It is used in various fields such as mechanics, electromagnetism, and waves to analyze and solve problems related to vibrations and oscillations.

## 5. Can the Simple Harmonic Motion equation be applied to other systems besides pendulums?

Yes, the Simple Harmonic Motion equation can be applied to other systems that exhibit oscillatory motion, such as a mass-spring system or a vibrating guitar string. As long as the motion is periodic, the equation can be used to analyze and predict its behavior.

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