Calculate the speed of galaxy emitting light of the wavelength $5.48\times {10}^{{}^{-7}}\mathrm{m}$ which when received on earth is measured to have a wavelength of $5.65\times {10}^{-7}m$.

Light from a nearby galaxy is emitted at a wavelength of $657\mathrm{nm}$ and is observed on earth at a wavelength of $654\mathrm{nm}$.

a. Deduce the speed of this galaxy.

Light from a nearby galaxy is emitted at a wavelength of $657\mathrm{nm}$ and is observed on earth at a wavelength of $654\mathrm{nm}$.

b. State what, precisely, can we deduced about the direction of the velocity of this galaxy.

In a binary star system, two stars orbit a common point and move so that they are always in diametrically opposite positions. Light from both stars reaches an observer on earth. Assume that both stars emit light of wavelength $6.58\times {10}^{-7}\mathrm{m}$.$$

a. When the stars are in the position shown in the diagram, the observer on earth measures a wavelength of light of $6.58\times {10}^{-7}\mathrm{m}$ from the stars. Explain why there is no Doppler shift in this case.

In a binary star system, two stars orbit a common point and move so that they are always in diametrically opposite positions. Light from both stars reaches an observer on earth. Assume that both stars emit light of wavelength $6.58\times {10}^{-7} \mathrm{m}$.

b. When the stars are in the position shown in the diagram, the observer on earth measures wavelengths in the received light $6.50\times {10}^{-7}\mathrm{m}$ and $6.76\times {10}^{-7}\mathrm{m}$. Determine the speed of each stars.

A ball of mass $\mathrm{m}$ is attached to two identical springs of spring constant $\mathrm{k}$ as shown. Initially, the springs have their natural lengths. The ball is displaced to a small distance to the right and then released. What is the period of oscillations of the ball?