A mass of 100 grams is attached to a spring whose constant is 1600 dynes/cm. After the mass reaches equilibrium, its support oscillates according to the formula h(t) = sin 8t, where h represents displacement from its original position. See Problem 39 and Figure 5.1.22.
- (a) In the absence of damping, determine the equation of motion if the mass starts from rest from the equilibrium position.
- (b) At what times does the mass pass through the equilibrium position?
- (c) At what times does the mass attain its extreme displacements?
- (d) What are the maximum and minimum displacements?
- (e) Graph the equation of motion.
39. A mass m is attached to the end of a spring whose constant is k. After the mass reaches equilibrium, its support begins to oscillate vertically about a horizontal line L according to a formula h(t). The value of h represents the distance in feet measured from L. See Figure 5.1.22.
- (a) Determine the differential equation of motion if the entire system moves through a medium offering a damping force that is numerically equal to β(dx/dt).
- (b) Solve the differential equation in part (a) if the spring is stretched 4 feet by a mass weighing 16 pounds and β = 2, h(t) = 5 cos t, x(0) = x'(0) = 0.
FIGURE 5.1.22 Oscillating support in Problem 39
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