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# Developing total energy, amplitude and maximum speed

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A mass M attached to an ideal spring with force constant k executes SHM on a horizontal frictionless table. It has a total energy of 1.0 Joule and amplitude .10 m, and its maximum speed when location x= 0, is 1.2 m/sec.
a. find k and M and the period T.
b. If the initial location of the mass is at x= +Xm, develop x(t), and v(t), and a(t).
c. If the initial location is at Xo = +.08 m, and decreasing, develop x(t).

https://brainmass.com/physics/velocity/developing-total-energy-amplitude-maximum-speed-18975

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Physics statements:
A. The total energy at any point is the sum of the potential energy in the spring, plus the kinetic energy of the moving mass.
B. When the mass is at rest, (at +Xm and at -Xm), its KE is zero, therefore the total energy is the PE of the spring at those points.
C. When the spring is unstressed, (at x=0), the PE is zero, therefore the total energy is the KE of the mass at that point.

Part a. Step 1.
At Xm, the total energy is expressed as:
(1) PEmax = .5 k Xm^2
Step 2.
Substituting givens into (1) you should find that: