# Maximum acceleration, frequency and mechanical energy of a spring

by jmgXD6
Tags: frequency of motion, maximum acceleration, mechanical energy, spring
 P: 17 1. When a 0.20-kg 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, friction-less 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.
 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.
 P: 17 But how would you get velocity?
P: 317

## Maximum acceleration, frequency and mechanical energy of a spring

The velocity at any time is simply the time derivative of the position.
 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?
 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.
 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.
 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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