2. A spring with a 4-kg mass has natural length 1 m and is maintained stretched to a length of 1.3 m by a force of 24.3 N. If the spring is compressed to a length of 0.8 m and then released with zero velocity, find the position of the mass at any time t.
10. As in Exercise 9, consider a spring with mass m, spring constant k, and damping constant c = 0, and let w = sqrt (k/m). If an external force F(t) = F0 cos wt is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to show that the motion of the mass is given by x(t) = c1 cos wt + c2 sin wt + (F0/(2mw))t sin wt.© BrainMass Inc. brainmass.com March 21, 2019, 1:50 pm ad1c9bdddf
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First we need to find the spring constant. Assume the equilibrium (no compress or stretch in the spring) is x=0.
When the spring is stretched to a length of 1.3 m, the displacement is x = 1.3- 1 = 0.3 m.
So the spring constant is .
Now based on the Newton's second law,
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By solving differential equations, It finds the motion equations of the mass, which is in simple harmonic oscillation driven by an external force. The solution is detailed and well presented.