Exercises 2–8: These exercises deal with undamped vibrations of a spring-mass system, my" + ky = 0, y(0) = yo- y'(0) = yo- (16) Use a value of 9.8 m/s² or 32 ft/sec? for the acceleration due to gravity. 2. A 10-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 30 mm. Assume the mass is then pulled down another 70 mm and released (with no initial velocity). (a) Determine the spring constant k. (b) State the initial value problem (giving numerical values for all constants) for y(t), where y(t) denotes the displacement (in meters) of the mass from its equilibrium rest position. Assume that y is measured positive in the downward direction. (c) Solve the initial value problem formulated in part (b).
Exercises 2–8: These exercises deal with undamped vibrations of a spring-mass system, my" + ky = 0, y(0) = yo- y'(0) = yo- (16) Use a value of 9.8 m/s² or 32 ft/sec? for the acceleration due to gravity. 2. A 10-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 30 mm. Assume the mass is then pulled down another 70 mm and released (with no initial velocity). (a) Determine the spring constant k. (b) State the initial value problem (giving numerical values for all constants) for y(t), where y(t) denotes the displacement (in meters) of the mass from its equilibrium rest position. Assume that y is measured positive in the downward direction. (c) Solve the initial value problem formulated in part (b).
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Please do #5
section 3.5
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