Set 9 Problem number 14

• Problem

• Solution

Problem

An ideal spring has unknown restoring force constant. An mass of 44.12 kg suspended from the spring is observed to oscillate at .6944 cycles/sec. What is the restoring force constant?

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 .6944 cycles every second. Since each cycle consists of 2 `pi radians, the object completes 2 `pi ( .6944) radians every second = 4.363 radians/second. This is the angular frequency.

Since we know k, we know that 4.363 radians/second = `sqrt[( 840 Newtons/meter) / m].

• Solving for m we obtain m = 840 Newtons/meter/( 4.363 radians/second) ^ 2 = 0 kilograms.

To solve symbolically, 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.