A sphere of mass m1 is attached to an ideal spring, then pulled downward from its equilibrium position and released from rest. A sphere of mass m2 is hung from a massless string of length L, pulled to the right from its equilibrium position, and released from rest. If both spheres have the same period of oscillation, then what is the spring constant of the spring attached to m1

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

Calculate the work done by an external agent during an isothermal compression of 1.00 mol of oxygen from a volume of 22.4 l at 10∘c and 1.0 atm pressure to 16.8l

Awave is produced in a rope. the wave has a speed of 33 m/s and a frequency of 22 hz. what wavelength is produced?