(a) Explanation Given information: The weight ( W ) of the block is 20 lb. The spring constant ( k ) of the both the spring A and B is 12 lb/in . . Assume the acceleration due to gravity ( g ) as 32.2 ft/s 2 . Calculation: Show the free body diagram of the system as in Figure (1): Write the expression for tension ( T ): Resolve the vertical component of force in pulley. ∑ F y = 0 − T − T + k y 0 2 = 0 2 T = k y 0 2 T = k y 0 4 Calculate the displacement ( y 0 ) : Resolve the vertical component of force in block. − 20 + k y 0 + T = 0 Substitute k y 0 4 for T . − 20 + k y 0 + k y 0 4 = 0 5 4 k y 0 = 20 Substitute 12 lb/in . for k . 5 4 ( 12 ) y 0 = 20 y 0 = 20 15 y 0 = 1.333 in . × 1 ft 12 in . y 0 = 1 9 ft Calculate the mass ( m ) of the block using the relation: m = W g Substitute 20 lb for W and 32.2 ft/s 2 for g . m = 20 lb 32.2 ft/s 2 = 0.621 lb ⋅ s 2 / ft For position 1: Write the expression for kinetic energy ( T 1 ) : T 1 = 0 Write the expression for potential energy ( V 1 ) : V 1 = 1 2 k 2 x 1 2 + 1 2 k 2 ( x 1 2 ) 2 For position 1: Write the expression for the velocity ( v 2 ) at position 2: v 2 = ω n x 1 Here, x 1 is the displacement. Write the expression for kinetic energy ( T 2 ) : T 2 = 1 2 m v 2 2 Substitute ω n 2 x 1 2 for v 2 (b) To determine The maximum velocity ( v m ) achieved by the block.

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Chapter 19.3, Problem 19.71P

(a)

To determine

The period (τn) of the resulting vibration.

(b)

To determine

The maximum velocity (vm) achieved by the block.

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Chapter 19.3, Problem 19.70P

Chapter 19.3, Problem 19.72P

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Chapter 19 Solutions

VECTOR MECHANIC

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - Prob. 19.6P Ch. 19.1 - Prob. 19.7P Ch. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

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The period ( τ n ) of the resulting vibration.

Solution Summary: The author shows the free body diagram of the system as in Figure (1): Write the expression for tension ( T): Resolve the vertical component of force in pulley.

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The period (τn) of the resulting vibration.

The maximum velocity (vm) achieved by the block.

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Chapter 19 Solutions