Maximum acceleration, frequency and mechanical energy of a springby jmgXD6 Tags: frequency of motion, maximum acceleration, mechanical energy, spring 

#1
May812, 01:44 PM

P: 17

1. When a 0.20kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.050m to 0.060m. The same block is attached to the same spring and placed on a horizontal, frictionless surface. The block is then pulled so that the spring stretches to a total length of 0.10m. The block is released at time t=0 s and undergoes simple harmonic motion.
0.20 kg [_]/\/\/\/\ ________spring 1. What is the maximum acceleration of the block? 2. What is the frequency of the motion? 3.What is the total mechanical energy of the system at any instant? F=mg=k/x a=(k/m)x ω=2∏/T Emechanical energy=U+k For acceleration it should be 98m/s because when the mass was hanging down the spring x=.010m and F=1.96 that would mean k=196 then plugged into a=k/m*x with .1 as x the answer should be 98m/s. I'm sure it's right, but let me know if I'm wrong. I'm having trouble though finding the other two answers, for frequency of motion I can't find time and for mechanical energy I can't find the equation for potential energy in a spring. 



#2
May912, 01:59 PM

P: 1,195

Mechanical energy (PE+KE) is constant in this system. That being the case, the derivative of it with respect to time is zero. Assume the displacement to be simple harmonic motion such as
x = A*sin(omega*t) Knowing that PE=(kx^2)/2 and KE=(mv^2)/2, you can proceed from there to get the natural frequency. 



#3
May912, 07:47 PM

P: 17

But how would you get velocity?




#4
May912, 09:56 PM

P: 317

Maximum acceleration, frequency and mechanical energy of a spring
The velocity at any time is simply the time derivative of the position.




#5
May1012, 08:14 AM

P: 17

I found v=+ or √(k/m)√A^2 x^2 with A equals the amplitude of motion but what's the amplitude of motion?




#6
May1012, 09:18 AM

P: 1,195

"v=+ or √(k/m)√A^2 x^2"
Where did you get the above expression? The x^2? The amplitude of the motion is given in the problem statement. 



#7
May1012, 09:32 AM

P: 17

It was in my physics book, the square root of k over m times the square root of A squared minus x squared. Is the amplitude of motion the same as x, .1 or is it .01? I just forgot to put it into parentheses.




#8
May1012, 10:40 AM

P: 1,195

"its original length of 0.050m ......The block is then pulled so that the spring stretches to a total length of 0.10m."
Problem states that the original length is 0.05m. So if it is initially streached to 0.10m, the amplitude is 0.05m. 


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