The maximum restoring force that can be applied to the disk without breaking it is 29,000 N. What is the maximum oscillation amplitude that won't rupture the disk?

The Amplitude is 7.34 × 10^6m

Explanation: complete question(The ultrasonic transducer used in a medical ultrasound imaging device is a very thin disk (m = 0.10 g) driven back and forth in SHM at 1.0 MHz by an electromagnetic coil.)

From Newton's 2nd law, the force F on a body with mass,m is related to its acceleration by:

F= ma ...eq1

The maximum transverse speed and acceleration of a particle in simple Harmonic motion are found in terms of the angular speed and amplitude

Vmax=wa ...eq2

amax= w^2A ...eq3

The angular frequency w of a wave is related to the frequency by:

w = 2pif ...eq4

Fmax= mw^2A

Fmax= m(2pif)^2A

Fmax= 4pi^2mf^2A

Where Fmax= maximum restoring force

m= mass of disk

f= frequency of disk

A= Fmax/[4pi^2×(0.10×10^-3)×(1.0×10^6)^2]

A= 29000/ [4x(3.142)^2×(0.10×10^-3)×(1.0×10^6)^2]

A= 29000/(3948865600)

A= 7.34×10^-6m

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

ya te mando la respuesta