Calculating Time for Block to Reach Max. Amp. After Spring Collision

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SUMMARY

The discussion centers on calculating the time it takes for a block, after being struck by a bullet, to reach maximum amplitude in a simple harmonic motion scenario. The block has a mass of 0.28 kg and is attached to a spring with a spring constant of 12 N/m, while the bullet has a mass of 4.4 g and an initial velocity of 53 m/s. The final velocity of the combined system after the collision is calculated to be 1.309 m/s. The maximum amplitude after the collision is determined to be 0.3246 m, and the time to reach this amplitude can be calculated using the equation x = Bsin(wt + alpha).

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Knowledge of conservation of momentum
  • Familiarity with the equations of motion for oscillating systems
  • Basic trigonometry for solving sinusoidal functions
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  • Calculate the angular frequency (ω) for the system using the spring constant and mass.
  • Learn how to derive the time period of simple harmonic motion.
  • Explore the implications of conservation of momentum in inelastic collisions.
  • Practice solving problems involving sinusoidal motion and phase angles.
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Homework Statement



A block of mass 0.28kg is attached to a spring of spring constant 12N/m on a frictionless track. The block moves in simple harmonic motion with amplitude 0.2m. While passing through the equilibrium point from left to right, the block is struck by a bullet, which stops inside the block. The velocity of the bullet immediately before it strikes the block is 53m/s and the mass of the bullet is 4.4g.
How long will it take for the block to reach maximum amplitude [which I calculated to be 0.3246) after the collision?

Homework Equations



M1V1 + M2V2 = (M1+M2)Vf
x = Bsin(wt+alpha)
I found Vf = 1.309 m/s

The Attempt at a Solution



I think the answer will have to solved using the equation, x = Bsin (wt + alpha), but I don't know what numbers to plug in for those. Any help would be greatly appreciated!
 
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I got the answer. :)
 

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