Q1. Find the solution of the following differential equation

d²y/dx² + ay = 0

Q2. Find the potential energy of the following system:

Assuming no friction or other forces act on the particle (except F).

Q3. A nano-particle is oscillating with the potential energy v(x) = 1/2mω²x².

Where, m is the mass of the atom, w is the frequency of oscillation and x is the displacement. Find the total energy of such system.

Q4. Can you establish a rule for the following sequence;

656.3x10^-9, 486.1x10^-9, 434.1 x10^-9, 410.2x10^-9, 397.0x10^-9, 388.9x10^-9, 383.5x10^-9, 364.6x10^-9