A Physical System that Oscillates

• Oscillations and Waves 2023 A mass \(m\) is strung on a very light wire equidistant between two anchor points separated by a distance \(2L\). When the mass is displaced laterally (i.e. plucked) in the \(x\)-direction (here vertically), there is constant tension \(T\) on the wire that produces a restoring force.

  

  1. What is the resulting natural frequency \(\omega_0\) of the oscillating mass? Assume tension drives the oscillation (i.e. no gravity, if it helps pretend you are looking down at a mass resting on a frictionless surface) and assume the angle the string makes with the posts is small.

     Note: \(\omega_0\) must be expressed in terms of the physical parameters given in the problem (\(T, L, m\)).

  2. Write a generic expression for displacement from equilibrium in any of the standard forms, \(ABCD\).