A 32.0 kg block at rest on a horizontal frictionlessair track is connected to th

Question

A 32.0 kg block at rest on a horizontal frictionlessair track is connected to the wall via a spring. The equilibriumposition of the mass is defined to be at x=0. Somebody pushes themass to the position x= 0.350 m, then lets go. The mass undergoessimple harmonic motion with a period of 4.40 s. What is theposition of the mass 3.564 s after the mass isreleased?Consider the same mass and springdiscussed in the previous problem. What is the magnitude of themaximum acceleration the mass undergoes during its motion?

Explanation / Answer

mass m = 32kg amplitude A = 0.35 m period T = 4.4 s time t = 3.564s Position of the mass at time t is x = A cost                                                    = 0.35 m cos ( 2t / T ) position of the mass 3.145 s after the mass is released x = 0.35 m cos ( 2(3.564 ) / 4.4 )                                                                                     = 0.1288 m maximum accleration a = A ^ 2                                   = A ( 2 / T ) ^ 2                                   = 0.7137 m / s ^ 2

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