Physics

${\lambda }_1=6MHz=6*10^{6}Hz$

${\lambda }_1=\frac{C}{{\upsilon }_1}=\frac{3*10^8}{6*10^6}=50m$

${\lambda }_2=\frac{C}{{\upsilon }_2}=10*10^6=\frac{3*10^8}{10*10^6}=30m$

Wavelength bandwidth

$=\left|{\lambda }_1-{\lambda }_2\right|=20m$

Given Acceleration of m₂ is 2m/s²

(upward)

N = 20a              T – m₂g = m₂a

T – 20g = 20a

T = 200 + 20 * 2

T = 240 N

T = m₁ a₁

240 = 10a₁

a₁ = 24 m/s²

$\Rightarrow Ta+T{a}_1-T{a}_2=0$

$a_2=24+2=26m/s^2$

F – T – N = Ma₂

F – 240 = 100 * 26 + 20 * 26

F = 3360 N

No, only oscillations with a linear restoring force and sinusoidal motion are SHM. Non-linear oscillations, such as large pendulum swings, deviate from SHM.

Oscillations are larger, slower to-and-fro motions. Vibrations, on the other hand, are smaller, faster oscillations. Vibrations often occur in machines, strings, and structural components.

No, periodic motion isn't always oscillatory. It may not involve back-and-forth movement about an equilibrium point. Some known examples include circular motion in satellites or planets. 

A simple pendulum shows simple harmonic motion only for small angular displacements. Otherwise, its motion is oscillatory but not purely SHM.

Tension in the string and gravitational force are common forces. These forces are resolved into tangential and radial components.

For small displacements,  sinθ≈θ (in radians), the small-angle approximation simplifies pendulum motion equations and makes it to approximate simple harmonic motion.

$A\to 286$

$Z=81$

Statement I is true as atoms are electrically neutral because they contain equal number of positive and negative charges.

Statement II is wrong as atom of most of the elements are stable and emit characteristic spectrum. But this statement is not true for every atom.