Opposing spring oscillation with mass

AI Thread Summary
To determine the frequency of oscillation for a 36 kg mass connected to two springs with constants k1 = 3 N/m and k2 = 4 N/m, it is essential to analyze the system's dynamics. The springs are positioned on opposite sides of the mass, meaning their effects cannot be simply added together. When the mass is displaced, the forces from each spring will act in opposite directions, influencing the net restoring force. The correct approach involves using the effective spring constant derived from the individual spring constants. This will allow for the calculation of the oscillation frequency using the formula for simple harmonic motion.
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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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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?
 
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