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Unformatted text preview: Engineering Mechanics  Dynamics Chapter 22 Problem 221 When a load of weight W 1 is suspended from a spring, the spring is stretched a distance d . Determine the natural frequency and the period of vibration for a load of weight W 2 attached to the same spring. Given: W 1 20 lb W 2 10 lb d 4 in Solution: k W 1 d k 60.00 lb ft Z n k W 2 g Z n 13.89 rad s W 2 S Z n W 0.45 s f Z n 2 S f 2.21 1 s Problem 222 A spring has stiffness k . If a block of mass M is attached to the spring, pushed a distance d above its equilibrium position, and released from rest, determine the equation which describes the blocks motion. Assume that positive displacement is measured downward. Given: k 600 N m M 4 kg d 50 mm Solution: Z n k M Z n 12.2 rad s v x d at t x A sin Z n t + , B cos Z n t + , . A B d Thus, x B cos Z n t + , B 0.05 m Z n 12.2 rad s 786 Engineering Mechanics  Dynamics Chapter 22 Problem 223 When a block of mass m 1 is suspended from a spring, the spring is stretched a distance # G 1 Determine the natural frequency and the period of vibration for a block of mass m 2 attached to the same spring. Given: m 1 3 kg m 2 0.2 kg G 60 mm g 9.81 m s 2 Solution: k m 1 g G k 490.50 N m Z n k m 2 Z n 49.52 rad s f Z n 2 S f 7.88 Hz r 1 f r 0.127 s *Problem 224 A block of mass M is suspended from a spring having a stiffness k . If the block is given an upward velocity v when it is distance d above its equilibrium position, determine the equation which describes the motion and the maximum upward displacement of the block measured from the equilibrium position. Assume that the positive displacement is measured downward. Given: M 8 kg k 80 N m v 0.4 m s d 90 mm Solution: Z n k M Z n 3.16 rad s x A sin Z n + , t B cos Z n + , t . B d A v Z n x A sin Z n + , t B cos Z n + , t . A 0.13 m B 0.09 m Z n 3.16 rad s 787 Engineering Mechanics  Dynamics Chapter 22 x max A 2 B 2 . x max 0.16 m Problem 225 A weight W is suspended from a spring having a stiffness k. If the weight is pushed distance d upward from its equilibrium position and then released from rest, determine the equation which describes the motion. What is the amplitude and the natural frequency of the vibration? Given: W 2 lb k 2 lb in d 1 in g 32.2 ft s 2 Solution: Z n k W g Z n 19.7 rad s y A cos Z n t + , B sin Z n t + , . A d B 0 in y A cos Z n t + , A 0.08 ft Z n 19.7 rad s f Z n 2 S f 3.13 Hz C A 2 B 2 . C 1.00 in Problem 226 A weight W is suspended from a spring having a stiffness k . If the weight is given an upward velocity of v when it is distance d above its equilibrium position, determine the equation which describes the motion and the maximum upward displacement of the weight, measured from the equilibrium position. Assume positive displacement is downward....
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 Spring '08
 Vandenbrink
 Natural Frequency

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