Question

51 A Block-Spring System A 320-g block connected to a light spring for which the force constant is 5.30 N/m is free to oscillate on a frictionless, horizontal surface. The block is displaced 5.10 cm from equilibrium and released from rest as in the figure. (A) Find the period of its motion. (B) Determine the maximum speed of the block. (C) What is the maximum acceleration of the block? (D) Express the position, velocity, and acceleration as functions of time in SI units. A block-spring system that begins its motion from rest with the block atx=Aat-0, In this case, ф-0; therefore, x A cos ut. SOLVE IT (A) Find the period of its motion. Conceptualize Study the figure and imagine the block moving back and forth in simple harmonic motion once it is released. Set up an experimental model in the vertical direction by hanging a heavy object such as a stapler from a strong rubber band. Categorize The block is modeled as a particle in simple harmonic motion. Analyze Use the equation to find the angular frequency of the block-spring system k 5.30 N/m 320 × 10-3 kg 4.07 rad/s Use the equation to find the period of the system: 21t 2π ㅡㅡ = :1 54378 a) 4.07 rad/s (B) Determine the maximum speed of the block. Use the equation to find vx: Ynax = aA (4.07 rad/s)(5.10 x 10.2 m) = 20757 m/s

Answer 1

(D = A Coscutto) do .051 Cos(4.07€) V = 0.20757 Sin (4.07€) 0.8448 cos(4.076) a = Master IT Position is maximum when da dt sv=o > 4.076 + 0.14511 = 1 =t=0.66/sec -o enhen v is moc., (b) du dt a=0 -> 4.07t+ +0.145 T = 311 필 t1.046/ see

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