OP-AMP RC multivibrator not producing a sine wave across capacitor.
You need to read your data sheet more closely. Specifically, read section 10. 


  The NE5532x and SA5532x devices are specified for operation over the
  range of ±5 to ±15 V


but you are trying to run it from a single +5 supply. So the op amp is not remotely happy. Furthermore, if you look at section 7.5, Maximum peak-to-peak output swing, you'll see that for +/- 15 volts the op amp is only guaranteed to swing +/- 12 volts, or within 3 volts of the power supply voltages. Notice that, if this applies to lower voltages (although there is no way to tell, since there is no spec for this, which ought to be an enormous red flag) there would be no output swing at all for power supplies less than 6 volts total. And this is pretty consistent with the 350 mV that you're getting.

Worse, there is no obvious reason for your oscillator to work. Consider the situation when the output transitions from low to high. The high output level both charges the capacitor AND sets the trigger level, so in theory it will take infinite time for the capacitor to charge to the point where it will trigger an output change. Given that real op amps have input voltage offsets, it would be perfectly possible for the capacitor never to reach a trigger voltage.

Furthermore, even if the circuit did work, why in the world would you expect a sine wave output? What you have made is a very bad version of a classic relaxation oscillator, and a square wave output is exactly what you'd expect. The capacitor voltage should then be exponential waveforms as the square wave charges and discharges it, and that (within the limits of your setup) is exactly what you're seeing.