Since it follows a simple harmonic motion then the
displacement of the oscillator follows the expression: x (t) = A cos (ω t + δ)
Then this gives that the formula for maximum acceleration is:
a = amax = A w^2
Where,
A = maximum amplitude of the wave
w = angular velocity
We also know that w is equivalent to: w = 2 π f
Therefore combining all and using the Newton’s 2nd
law of motion:
F = m a
F = m A w^2
F = m A (2 π f)^2
A = F / m (2 π f)^2
Plugging in the given numbers:
A = 40,000 N / [(10^−4 kg) (2 π * 10^6 / s)^2]
A = 1.0132 * 10^-5 m
or simplifying
A = 10^5 m = 10 microns
