Set 9 Problem number 11

• Problem

• Solution

Problem

What is the mass in kilograms of an object which oscillates at .6802 cycles / sec when suspended from an ideal spring whose restoring force constant is 130 Newtons/meter?

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 .6802 cycles every second. Since each cycle consists of 2 `pi radians, the object completes 2 `pi ( .6802) radians every second = 4.274 radians/second. This is the angular frequency.

Since we know k, we know that 4.274 radians/second = `sqrt[( 130 Newtons/meter) / m].

• Solving for m we obtain m = ( 130 Newtons/meter) / ( 4.274 radians/second) ^ 2 = 7.116 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.