In the double-spring horizontal mass spring system, can I still apply the SHM equations $a=-\omega^2x$ and $T=2π\left(\frac{m}{k}\right)^{1/2}$?
[Physics] double-spring horizontal mass spring system
spring
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Best Answer
In equilibrium assume that both springs are in a state of tension.
The two springs exert equal magnitude but opposite direction forces on the mass; the left hand spring exerts a force to the left and the right hand spring exerts a force to the right.
When the mass moves to the left away from the equilibrium position the left hand spring exerts a smaller force to the left and the right hand spring exerts a larger force to the right.
Now a smaller force to the left is equivalent to a larger force to the right so the net effect is that magnitude of the force on the mass due to the two springs is twice that due to one spring and the direction is to the right.
So what is the effective spring constant of the two springs in this arrangement as compared with the spring constant of one spring $k$?