Problem: A mass on a spring is observed to complete 96 cycles of oscillation in a minute. The spring constant is 23 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 completes 96 cycles in 60 seconds. Thus the object completes 2 `pi ( 96) radians in 60 seconds. This implies a rate of 2 `pi ( 96) radians/60 seconds = 10.05 radians/second.
Since we know k, we know that 10.05 radians/second = `sqrt[( 23 Newtons/meter) / m].
Solving for m we obtain m = 23 Newtons/meter/( 10.05 radians/second) ^ 2 = .2277 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.