be detailed please We reconsider the mass-spring system but now assume there is

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be detailed please

We reconsider the mass-spring system but now assume there is a frictional force present and this frictional force is proportional to the velocity of the particle. Thus the force acting on the particle comes from two terms: one due to the force exerted by the spring and the other due to the frictional force. Thus Newton's equations become -kx - beta x = mx where as before x = :r(t) is the displacement from the equilibrium position at time t. beta and k are positive constants. Introduce the energy function E = E(x,x) = 1/2mx2 = + 1/2kx2, and show that if x = x(t) satisfies (2.31), then dE/dt

Explanation / Answer

1.
KE = m(x')

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