A vibration platform oscillates up and down with a fixed amplitude of 9.7 cm and a controlled frequency that can be varied. If a small rock of unknown mass is placed on the platform, at what frequency will the rock just begin to leave the surface so that it starts to clatter?

1.6 Hz

Explanation:

In simple harmonic motion, acceleration is given by the formula;

a = Aω²

Where;

A is amplitude

ω is angular velocity.

We are given A = 9.7 cm = 0.097 m

We know that acceleration due to gravity is 9.8 m/s².

Thus;

9.8 = 0.097ω²

ω² = 9.8/0.097

ω = √101.031

ω = 10.05 rad/s

Formula for frequency is;

f = ω/2π

Thus;

f = 10.05/2π

f = 1.6 Hz

b. a lightning bug, plug of grass, and a worm