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Springs in series/parallel oscillations
Intermediate
Equivalent stiffness changes the frequency.
Effective stiffness changes the frequency: parallel k = k₁ + k₂ (higher f), series 1/k = 1/k₁ + 1/k₂ (lower f).
Two 20 N/m springs in parallel: ω rises by √2.
Check how the springs are connected to the mass.
In more detail
Springs in series or parallel change the effective spring constant, which changes the oscillation frequency. Parallel springs stiffen the system, and series springs soften it.
Real-world uses
- Designers combine springs to tune the natural frequency of machines.
- Car suspensions use springs in parallel to share loads.
- Engineers combine springs to adjust the natural frequency of a machine mount so that it avoids dangerous resonances.
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Frequently asked questions
Which increases frequency?
Springs in parallel, because the effective spring constant is larger.
How do I find the effective constant?
Add the constants for parallel springs, and use reciprocal sums for series springs.
How do combined springs change the frequency?
Stiffer combinations give a higher frequency, while softer ones give a lower frequency, since the frequency depends on the square root of the stiffness.
Related topics in Oscillations & SHM
Phasor representation · Mass–spring system · Vertical spring · Simple pendulum · Small-angle approximation · Pendulum at large amplitude