To measure the magnitude of the acceleration due to gravityg in an unorthodox manner, a studentplaces a ball bearing on the concave side of a flexible speakercone.
The speaker cone acts as a simple harmonic oscillator whoseamplitude is A and whose frequency f can be varied.

The student can measure bothA and f with a strobe light. Take the equation ofmotion of the oscillator as

y(t)=A\cos{(\omega t+\phi )},

where \omega = 2\pi f and the yaxis points upward.

If the ball bearing has mass m, find N(t), the magnitude of the normalforce exerted by the speaker cone on the ball bearing as a functionof time.

Your result should be in terms ofA, f (or omega), m, g, a phase angle phi, and the constant pi.