The physics
A spring pulls back with F = −kx. So the block's acceleration is a = −(k/m)x. That is simple harmonic motion (SHM).
ω = √(k/m) T = 2π√(m/k)
One beat is one full swing. A heavier block swings slower. A stiffer spring swings faster. The size of the swing does not change the beat.
Springs in a line share one pull, so they are softer together. Springs side by side, or one on each side, share one stretch. So they are stiffer together.
in a line: 1/k = 1/k₁ + 1/k₂ side by side: k = k₁ + k₂
A spring that is stiff one way gives two half swings. Add their times. A steady push moves the centre to F/k. It does not change the beat.
Two carts on one spring swing about their centre of mass. Use the reduced mass μ in place of m. The light cart moves more.
μ = m₁m₂/(m₁ + m₂) T = 2π√(μ/k) m₁A₁ = m₂A₂