Set 9 Problem number 11

• Problem

• Solution

Problem

An ideal spring has restoring force constant 670 Newtons/meter. An unknown mass on the spring is observed to oscillate at .4065 cycles/sec. What is the mass, in kilograms?  

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 .4065 cycles every second. Since each cycle consists of 2 `pi radians, the object completes 2 `pi ( .4065) radians every second = 2.554 radians/second. This is the angular frequency.

Since we know k, we know that 2.554 radians/second = `sqrt[( 670 Newtons/meter) / m].

• Solving for m we obtain m = ( 670 Newtons/meter) / ( 2.554 radians/second) ^ 2 = 102.7 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.