PHYSICS 306 – FINAL EXAM PRACTICE PROBLEMS (I) Problem 1

```PHYSICS 306 – FINAL EXAM PRACTICE PROBLEMS (I)
Problem 1
Two equal masses, of mass m, are connected as shown with identical massless springs of
spring constant k. Consider that the only motion is in the vertical direction.
a) Derive the equations of motion for this system
b) Find the frequencies of the normal modes for this system
Note: you do not need to consider gravity in this problem since it only affects the
equilibrium position of the system but not the dynamics.
Problem 2
A sinusoidal wave of amplitude 3m travels with a frequency of 10 Hz on a string of linear
mass density =0.2 kg m-1, length 10m and tension 10N.
a) Write an expression for the wave transverse displacement
b) Calculate the wave speed and wave number
c) Write down the complete waveform.
d) Light can be characterized as sinusoidal electromagnetic waves. If we consider
light passes normally through a glass plate (n=1.5) suffering only one air to glass
and one glass to air reflection. What is the loss of intensity?
Problem 3
Suppose that we’re interested in measuring the spectrum of a light wave, E(t), which in
~
nothing but the Fourier transform E ( )  [ E (t )]
Somehow a small fraction of the irradiance of this light, say ε, takes a different path that
also leads to the spectrometer. The extra light has the field, √ ε E(t–a), where a is the extra
path taken by the weak beam. Calculate the measured spectrum.
```