Question

You can observe the main effects of resonance with very simple experiments. Hold a spring vertically with a mass suspended at the other end, and observe the frequency of “free” oscillations with your hand kept still. Then stop the oscillations, and move your hand extremely slowly up and down in a kind of slow sinusoidal motion. You will see that the mass moves up and down with the same very low frequency. (a) How does the amplitude (plus or minus displacement from the center location) of the mass compare with the amplitude of your hand? (Notice that the phase shift of the oscillation is 0◦; the mass moves up when your hand moves up.) (b) Next move your hand up and down at a significantly higher frequency than the free-oscillation frequency. How does the amplitude of the mass compare to the amplitude of your hand? (Notice that the phase shift of the oscillation is 180◦; the mass moves down when your hand moves up.) (c) Finally, move your hand up and down at the free-oscillation frequency. How does the amplitude of the mass compare with the amplitude of your hand? (It is hard to observe, but the phase shift of the oscillation is 90◦; the mass is at the midpoint of its travel when your hand is at its maximum height.) (d) Change the system in some way so as to increase the air resistance significantly. For example, attach a piece of paper to increase drag. At the free-oscillation frequency, how does this affect the size of the response? A strong dependence of the amplitude and phase shift of the system to the driving frequency is called resonance.

Short answer

a) It is shown that the outside force is not affecting the amplitude of mass because it is not close to amplitude.

b) The amplitude of mass is reduced due to the amplitude of outside force is increased leading increase in amplitude of free oscillation.

c) The amplitude of mass will increase with time because the energy supplied by our hand to the mass spring system is largest at its regime.

d) The effect of resonance is slowed down.

Step-by-step solution

Identification of given data

The given data can be listed below,

• Phase shift when hand moves up is,$0°$.
• Phase shift when hand moves up and down is,$180°$.

Concept/Significance of the oscillation

The oscillation is the process of shifting from one position to another and again. An example is a pendulum oscillation swinging side to side.

(a) Determination of effect of the amplitude of the mass compare with the amplitude of your hand

The response to outside force in the phase without any change in the mass amplitude. Amplitude of oscillation is similar to the amplitude of free oscillation.

The graph shows difference between outside force and phase difference of the system.

Thus, it is shown that the outside force is not affecting the amplitude of mass because it is not close to amplitude.

Step 4: (b) determination of the effect the amplitude of the mass compared to the amplitude of your hand

In this case, the frequency of resonance is less than theoutside force. Because of that the amplitude of outside force is increased leading increase in amplitude of free oscillation.

Thus, the amplitude of mass is reduced.

(c) Comparison of amplitude of the mass with the amplitude of your hand

The amplitude of mass will increase with time because the energy supplied by our hand to the mass spring system is largest at its regime it is due to the fact that if outside force frequency is equal to free oscillation frequency of the mass whatever be the value of outside force.

(d) Determination of affect the size of the response when change the system in some way so as to increase the air resistance

If air resistance is included in energy dissipation the effect of resonance is slowed down.