A mass oscillating at the end of a spring

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SUMMARY

The discussion centers on the dynamics of a mass oscillating at the end of a spring, specifically a 250-g object with a spring constant of 4.80 N/m. The user calculated the acceleration at a displacement of 4.27 cm to be 8.10 m/s² upward, using the formula a = kx/m. However, there was a critical error in the spring constant value, which was mistakenly noted as 48 N/m instead of the correct 4.80 N/m. Additionally, the user sought assistance in determining the maximum speed of the object and the position at which this speed occurs.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Basic knowledge of Newton's second law of motion (F=ma)
  • Familiarity with oscillatory motion concepts
  • Ability to perform unit conversions (grams to kilograms)
NEXT STEPS
  • Review the principles of Hooke's Law and its application in oscillatory systems
  • Learn how to calculate maximum speed in simple harmonic motion
  • Study the relationship between displacement and velocity in oscillating systems
  • Explore the effects of varying spring constants on oscillation characteristics
USEFUL FOR

Physics students, mechanical engineers, and anyone studying dynamics and oscillatory motion will benefit from this discussion.

Trinity Nicole
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1. A 250-g object hangs from a spring and oscillates with an amplitude of 5.42 cm. The spring constant is 4.80 N/m.
a) What is the acceleration of the object when the displacement is 4.27 cm [down]?

I put:
m=0.25 kg
d=0.0542 m
k=48 N/m
x=0.0427m
Therefore:
F=kx which leads to a=kx/m
a=(48 N/m)(0.0427 m)/0.25 kg
a=8.10 m/s^2 [up]
b) What is the maximum speed of the object?
I put:
m=0.25 kg
d=0.0542 m
k=48 N/m
x=0.0427m
a=8.10 m/s^2 [up] (I think)
Not sure which equation to use...
c) At what position will the maximum speed occur?
I'd need B to know this, please help me out.
Thanks in advance!
 
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Trinity Nicole said:
k=48 N/m

It looks like you have a typo there -- can you re-check the problem statement? :smile:
 
berkeman said:
It looks like you have a typo there -- can you re-check the problem statement? :smile:
i'm sorry, what is my typo?
 
Trinity Nicole said:
The spring constant is 4.80 N/m.

Trinity Nicole said:
k=48 N/m

:smile:
 
There is another error in the OP solution to a).
In the equation F=ma, F is the net of all forces in the direction of the acceleration. What are all the forces acting on the mass?
 

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