A mass is vibrating at the end of a spring of force constant 225 N/m. Figure E14

Question

A mass is vibrating at the end of a spring of force constant 225 N/m. Figure E14.62 shows a graph of its position x as a function of time t. At what limes is the mass not moving? How much energy did this system originally contain? How much energy did the system lose between t = 1.0 s and t = 4.0 s? Where did this energy go?

Explanation / Answer

a) The mass is not moving when it is at its extreme position as it is momentarily at rest at that instant. i.e. at t = 0,1,2,3,4 sec b) Originally at t = 0 it is at extreme point (x = 7 cm). We can consider that it has only potential energy at that point. We know energy E=0.5*k*x*x => 0.5*225*(0.07)2 = 0.55125 J c) At t=1 and t=4 sec the mass is at its extreme point, so to calculate the change we calculate the difference in its potential energies. Energy change = 0.5*225*[(0.03)2 * (0.06)2] => -0.30375 J

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