Set 9 Problem number 12

• Problem

• Solution

Problem

What is the mass in kilograms of an object if, when suspended from an ideal spring whose restoring force constant is 580 Newtons/meter, the mass completes 499.98 cycles every minute?

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 499.98 cycles every minute.    This implies a frequency of 499.98 cycles/minute * 1 mimute / 60 sec = 8.333 cycles / sec.
• Since each cycle consists of 2 `pi radians, the object completes 2 `pi ( `freq) radians every second = 52.36 radians/second. This is the angular frequency.

Since we know k, we know that 52.36 radians/second = `sqrt[( 580 Newtons/meter) / m].

• Solving for m we obtain m = ( 580 Newtons/meter) / ( 52.36 radians/second) ^ 2 = .2115 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.