The maximum restoring force that can be applied to the disk without breaking it is 40000 n. what is the maximum oscillation amplitude that won't rupture the disk

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