To measure the magnitude of the acceleration due to gravity in an unorthodox man

Question

To measure the magnitude of the acceleration due to gravity in an unorthodox manner, a student places a ball bearing on the concave side of a flexible speaker cone (Figure 1) . The speaker cone acts as a simple harmonic oscillator whose amplitude is and whose frequency can be varied. The student can measure both and with a strobe light. Take the equation of motion of the oscillator as , where and the y axis points upward. Part A If the ball bearing has mass , find , the magnitude of the normal force exerted by the speaker cone on the ball bearing as a function of time. Your result should be in terms of , either (or ), , , a phase angle , and the constant .

Explanation / Answer

The ball bounces when the acceleration of the ball exceeds that of gravity. If A and fb are measured at that point, g = accel = A*w^2 = A*(2pi*fb)^2.

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