Period of Oscillation for vertical spring

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SUMMARY

The period of oscillation for a mass-spring system can be calculated using the formula T=2π√(m/k), where m is the mass (0.25 kg) and k is the spring constant (10 N/m). While gravity does influence the system by affecting the equilibrium position, it does not alter the formula for the period of oscillation in the context of small oscillations. The discussion emphasizes that the same equations used for horizontal springs apply to vertical springs, provided the effects of gravity are understood in terms of equilibrium position rather than period calculation.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Basic knowledge of oscillatory motion and period calculation
  • Familiarity with Newton's second law (ƩF=ma)
  • Concept of angular frequency in oscillatory systems
NEXT STEPS
  • Study the derivation of the period of oscillation for mass-spring systems
  • Learn about the effects of gravitational forces on oscillatory motion
  • Explore the concept of equilibrium position in vertical spring systems
  • Investigate advanced topics in harmonic motion, such as damping and resonance
USEFUL FOR

Students in physics, particularly those studying mechanics, as well as educators and anyone interested in understanding the dynamics of mass-spring systems in gravitational fields.

conniebear14
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Homework Statement



A mass m=.25 kg is suspended from an ideal Hooke's law spring which has a spring constant k=10 N/m. If the mass moves up and down in the Earth's gravitational field near Earth's surface find period of oscillation.

Homework Equations



T=1/f period equals one over frequency
T= 2pi/w two pi/angular velocity
f=w/2pi
w= (k/m)^1/2
T=2pi/sqrt(k/m)

The Attempt at a Solution



Using these equations I found periods for springs that were horizontally gliding, my question is can I use these same formulas for a vertical spring? Does gravity have to be taken into account?
 
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conniebear14 said:
Does gravity have to be taken into account?
Yes. Since it partly offsets the tension in the spring, it could affect the period. But I'm not asserting that it does. Think about where the mid point of the oscillation will be in terms of spring extension.
 
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Okay, for this problem let's not take gravity into account. Are my equations correct? Can I use the same approach that I used for a horizontal spring?
 
conniebear14 said:
Okay, for this problem let's not take gravity into account.
I don't understand. I thought I just advised you to take gravity into account. Just write down the equation for ƩF=ma.
 

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