Problem: A mass on a spring is observed to oscillate with a frequency of 4.2 cycles per second. The spring constant is observed to be 26 Newtons/meter. What is the mass, in kilograms?
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Solution: We know that the angular frequency of an object in simple harmonic motion is `sqrt(k/m). The angular frequency must be expressed in radians/second.
The information given is that the object 4.2 cycles every second. Since each cycle consists of 2 `pi radians, the object completes 2 `pi ( 4.2) radians every second = 26.38 radians/second. This is the angular frequency.
Since we know k, we know that 26.38 radians/second = `sqrt[( 26 Newtons/meter) / m].
Solving for m we obtain m = 26 Newtons/meter/( 26.38 radians/second) ^ 2 = .03736 kilograms.
In symbols, we solve `omega = `sqrt(k/m) for m, obtaining m = k / `omega ^ 2, then substitute the known values of k and the `omega found above.