I will show the question as a picture. To measure the magnitude of the accelerat

Question

I will show the question as a picture.

To measure the magnitude of the acceleration due to gravity g 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 A and whose frequency f can be varied. The student can measure both A and f with a strobe light. Take the equation of motion of the oscillator as y(t) = A cos (omega + phi), where omega = 2pi f and the y axis points upward.

Explanation / Answer

Ftotal = Fg + N(t)

Fg will be negative

Ftotal = ma

equation y(t) of motion is a position vs. time, take it's derivative twice to get acceleration vs. time. a(t)

then Ftotal = ma(t)

or: ma(t) = Fg + N(t)
ma(t) = -mg + N(t)
N(t) = mg - ma(t)

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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