The schematic figure at right shows a view-from-above for a mass-spring system.

Question

The schematic figure at right shows a view-from-above for a mass-spring system. The square mass, shown in the center, is connected to two immobile anchors (the circles at the top and the bottom) by two springs. The mass rides on a frictionless air table. The mass is displaced upwards in the figure and then released from rest.

a) What is the mass of the weight in grams?

b)What is the natural (same as resonant) frequency of this mass-spring system?

c) What is the period of this mass-spring system?

The schematic figure at right shows a view-from-above for a mass-spring system. The square mass, shown in the center, is connected to two immobile anchors (the circles at the top and the bottom) by two springs. The mass rides on a frictionless air table. The mass is displaced upwards in the figure and then released from rest. What is the mass of the weight in grams? What is the natural (same as resonant) frequency of this mass-spring system? What is the period of this mass-spring system?

Explanation / Answer

a) m (in grams) = W/g = 4.90*1000/9.8 = 500 g

c) Period = 2*pi*sqrt(m/Keff)

= 2*3.14*sqrt(0.5/(k1+k2))

= 2*3.14*0.158

= 0.9924 sec

b)

Natural Frequency = 1/(Period)

= 1/0.9924

= 1.007 Hz

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