Tricky spring problem. Amplitudes and AccelerationMax

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SUMMARY

The discussion focuses on a physics problem involving a mass-spring system, specifically a block with a mass of 6.7 kg suspended from a vertical spring that stretches 0.26 m in equilibrium. The block is initially pushed downward with a velocity of 4.7 m/s, leading to oscillations without friction. Key calculations include the spring constant (K = 252.54 N/m) and oscillation frequency (ω = 0.9771 rad/s). The amplitude of oscillation is determined to be 0.7655 m, and the maximum acceleration can be calculated using the formula aMax = ω² * A.

PREREQUISITES
  • Understanding of mass-spring systems and Hooke's Law
  • Familiarity with oscillation frequency and angular frequency (ω)
  • Knowledge of kinematics equations for oscillatory motion
  • Basic calculus for deriving velocity and acceleration from position functions
NEXT STEPS
  • Study the derivation of the spring constant (K) from mass and displacement
  • Learn about energy conservation in oscillatory systems
  • Explore the effects of damping on oscillations in spring systems
  • Investigate the relationship between amplitude, frequency, and maximum velocity in harmonic motion
USEFUL FOR

Students studying classical mechanics, physics educators, and anyone interested in understanding oscillatory motion in mass-spring systems.

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Homework Statement



A block with mass m =6.7 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.26 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.7 m/s. The block oscillates on the spring without friction.

3)After t = 0.4 s what is the speed of the block?
4)What is the magnitude of the maximum acceleration of the block?

Calculated K = 252.5384615
Oscillation Frequency (omega) = .9771168341

Homework Equations



Amplitude = vMax*sqrt(m/k)



The Attempt at a Solution


I got amplitude to be 0.7655.
I used -(omega)*Acos(omega*t) to find V for number 3. I used aMax = omega^2*t
 
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I believe there is an equation that you use to find the velocity at any given point given amplitude, stretched distance, k and mass. hold on... so its the sqrt(k/m) times the sqrt(amplitude^2 - stretched or compressed distance^2) use that
 
oh nevemind. use 9.8m/s^2(t) to find the speed after sometime. isn't the acceleration the same?
 

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