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Mass–spring system
Beginner
Mass on a spring oscillates with period set by m and k.
T = 2π√(m/k)T = 2π√(m/k). Heavier mass or softer spring gives a longer period. It doesn't depend on amplitude (within Hooke's law).
m = 0.5 kg, k = 50 N/m: T = 0.63 s.
Spring's own mass is ignored.
In more detail
A mass on a spring oscillates with angular frequency ω = sqrt(k/m) and period T = 2π sqrt(m/k). The period depends on mass and spring constant but not on amplitude.
Real-world uses
- Car suspension systems are designed with specific spring constants and masses.
- Mechanical watches use balance springs to set their timing.
- A car's suspension spring with a given mass has a natural period that engineers can tune by choosing the spring stiffness.
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Frequently asked questions
Does a larger mass make it slower?
Yes, the period increases with the square root of the mass.
Does amplitude matter?
Not in the ideal case, since the period is independent of amplitude.
Does a heavier mass oscillate more slowly?
Yes. A larger mass on the same spring has a longer period, because the inertia is greater.
Related topics in Oscillations & SHM
Phase and phase constant · Phase difference · Phasor representation · Vertical spring · Springs in series/parallel oscillations · Simple pendulum