Using Simple Harmonic motion and conservation of motion to find maximum velocity

AI Thread Summary
The discussion focuses on using conservation of energy principles to determine maximum velocity in simple harmonic motion. The key equations referenced include kinetic energy, potential energy, and the relationship between them at the equilibrium point. The solution involves analyzing energy at different points, concluding that maximum kinetic energy occurs when potential energy is at a minimum. The calculated maximum velocity is approximately 68.59 m/s, derived from the energy conservation equation. The discussion emphasizes the importance of understanding equilibrium and periodicity in oscillatory motion for solving similar problems.
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The Question
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Relevant equations
KE=0.5*m*v^2
T=2*pi*sqrt(m/k)
EE=0.5*k*x^2
KEi+UEi=KEf+UEf
I think that's all of them

attempt at a solution
I was thinking about just using the conservation of energy at the the equilibrium point, as the kinetic energy would be at a max there and the potential energy would be at its minimum, Also the velocity would be at its max while the acceleration would be zero. However, one of the many problems I've run into on this question is that I'm unsure if the average of the two x values will give me the equilibrium point (if it did then it would be 5mm) and I don't feel comfrontable moving on having possibly made a false assumption.
 
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I got the answer :) but for others what I did was
from the graph u can see that potential at highest point is 5J and at lowest point is 1J

mgh+ 1/2mU^2 = mgH + 1/2 mV^2 in this U = initial velocity = 0 and V = max velocity at lowest point and mgh is initial potential energy and mgH is potential energy at lowest point.
this gives
5 + 0 = 1 + (1/2 x (1.7/1000) x V^2) [ 1.7 is divided by 1000 to convert grams into kg]
V^2 = 4705.88
V = sqrt(4705.88)
V = 68.59 m/s
 
Remember one thing- All the oscillations have two things in common
I. the oscillation takes place about an equilibrium position and,
II. the motion is periodic.

These are the only two conditions that are to be fulfilled for a motion to be oscillatory motion.
 
Thanks I'll keep that in mind in similar problems, my finals coming up soon it may come in handy
 
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