Respuesta :
Explanation:
It is given that,
Mass of the disk, [tex]m = 0.1\ g = 10^{-4}\ kg[/tex]
Frequency of SHM, [tex]f=1\ MHz=10^6\ Hz[/tex]
(A) Maximum restoring force, F = 30,000 N
We need to find the maximum oscillation in the amplitude that won't rupture the disk. We need that maximum acceleration of the particle in SHM is :
[tex]a_{max}=A\omega^2[/tex]
A is the amplitude of oscillation
[tex]\omega=2\pi f[/tex] is the angular frequency
Also, F = ma
So, [tex]F=mA\omega^2[/tex]
[tex]A=\dfrac{F}{4\pi^2mf^2}[/tex]
[tex]A=\dfrac{30000}{4\pi^2\times 10^{-4}\times (10^6)^2}[/tex]
[tex]A=7.59\times 10^{-6}\ m[/tex]
(B) The maximum speed in SHM is given by :
[tex]v=A\times \omega[/tex]
[tex]v=7.59\times 10^{-6}\times 2\pi \times 10^6[/tex]
v = 47.68 m/s
Hence, this is the required solution.
