A 0.450 kg object attached to a springwith a force constant of 8.00 N/m vibrates

Question

A 0.450 kg object attached to a springwith a force constant of 8.00 N/m vibrates in simple harmonicmotion with an amplitude of 12.5 cm. (a) Calculate the maximum value (magnitude) ofits speed and acceleration.

(b) Calculate the speed and acceleration when the object is7.50 cm from the equilibrium position.

(c) Calculate the time interval required for the object to movefrom x = 0 to x = 6.50cm. (a) Calculate the maximum value (magnitude) ofits speed and acceleration.

(b) Calculate the speed and acceleration when the object is7.50 cm from the equilibrium position.

(c) Calculate the time interval required for the object to movefrom x = 0 to x = 6.50cm.

Explanation / Answer

   a) The maximum value of the speed is              vmax = A Here A = 12.5 cm =0.125m          =(k/m)             k = 8.00 N/m            m = 0.450 kg The maximum acceleration is           amax = A^2 b) The speed of the object is          v=[A2 -x2] The acceleration of the object is           a =-Ax Substitute the values. c)

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