Opposing spring oscillation with mass

In summary, a 36 kg mass on a horizontal frictionless surface is connected to two springs with spring constants k1 = 3 N/m and k2 = 4 N/m. The frequency of oscillation of the mass can be calculated by using energy equations and SHM equations after drawing a free body diagram and considering the forces acting on the mass when it is displaced from equilibrium. The springs cannot be added together since they are on opposite sides of the mass.
  • #1
smhippe
19
0

Homework Statement


A 36 kg mass is placed on a horizontal frictionless surface and then connected to
walls by two springs with spring constants k1 = 3 N/m and k2 = 4 N/m. What is the
frequency, f (in Hz), of oscillation for the 36 kg mass if it is displaced slightly to one
side?


Homework Equations





The Attempt at a Solution


So, I wasn't sure if the spring constant added linearly or if something crazy happened. If it did then I was thinking it would be possible to plug in some numbers into the energy equations. From there plug it into the SHM equations. I'm not sure if that works at all though. Thanks!
 
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  • #2
Start by drawing a free body diagram.

The springs are on opposite sides of the mass, so you can't just add them.

In equilibrium, the initial extension is zero. So if you displace it x to one side, how will the forces act?
 

1. What is opposing spring oscillation with mass?

Opposing spring oscillation with mass is a phenomenon that occurs when a mass is attached to a spring and the spring is stretched or compressed, causing the mass to move back and forth in a repetitive motion.

2. How does the mass affect the oscillation of the spring?

The mass attached to the spring affects the oscillation by changing the period and amplitude of the oscillation. The larger the mass, the longer the period and the smaller the amplitude.

3. What factors affect the frequency of the oscillation?

The frequency of the oscillation is affected by the spring constant, the mass attached, and the initial displacement of the mass from equilibrium.

4. How can opposing spring oscillation with mass be used in practical applications?

Opposing spring oscillation with mass is used in many practical applications such as in shock absorbers, seismometers, and musical instruments. It is also used in studying the behavior of systems in physics and engineering.

5. How does the damping of the system affect the oscillation?

The damping of the system, which is the resistance to the motion of the mass, affects the amplitude of the oscillation. A higher damping will result in a smaller amplitude and a quicker decrease in the oscillation over time.

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