Question

A mass is on a driver with a spring. Using the module, turn on gravity and change the spring constant to 300N/m. Click and drag the frequency dial to change the driving frequency. How can you find the resonant frequency doing this? What is the value you get?

Use this link for the module: https://phet.colorado.edu/sims/resonance/resonance_en.html

Answer 1

To find the resonant frequency, we can keep increasing the driving frequency. The amplitude will gradually increase. Around 1.7 Hz one starts to see some significant increase in the amplitude. Now one can go in small steps and reach to the value of the resonant frequency by incrementing the driver frequency in small steps and checking if the amplitude increases or decreases. The maximum amplitude is reached at 1.732 Hz which is equal to the natural frequency of the spring-mass system.

Explanation:

The default settings are not changed except for the ones mentioned in the question. Spring constant is set to 300 N/m. When gravity is turned on the mass moves down due to gravity and the oscillations start. The driver is oscillating at 1 hz which means once a second. If we notice the vibrations patiently, we see that after some time the driver and the mass vibrate in phase i.e when the driver moves up, the mass moves up and when it moves down, the mass moves down. We can really see the role of the driver in "driving" the mass. But gradually, in several seconds, we see that they go out of phase i.e. when the driver tries to push the block up, the block or the mass is coming down. This leads to slowing down of the mass. To see this more clearly, one can increase the amplitude of the driver. Observing more closely, one can see that the spring is vibrating at a faster rate and it goes in and out of phase with respect to the driver. As we increase the driving frequency, the two remain more and more in phase. At the resonant frquency, the driver goes up and down at the same rate as is the natural frequency of the spring-mass system leading to resonance.