Spring-mass Oscillator

A mass attached to an ideal spring executes SHM with time period $T=2\pi \sqrt{m/k}$, where $m$ is the oscillating mass and $k$ is the spring constant. This follows because the spring supplies a linear restoring force $F=-kx$, giving angular frequency $\omega =\sqrt{k/m}$. Substituting $m=0.8\text{ kg}$ and $k=200\text{ N/m}$ yields $T=2\pi \sqrt{0.8/200}=2\pi \sqrt{0.004}=2\pi \times 0.0632\approx 0.40\text{ s}$. The value $0.13\text{ s}$ wrongly drops the factor $2\pi$ and reports only $\sqrt{m/k}$ scaled incorrectly. The value $0.63\text{ s}$ comes from inverting the ratio to $\sqrt{k/m}$ inside the root in part. The value $1.26\text{ s}$ doubles the correct period, a common slip from using $4\pi$ instead of $2\pi$. This is the textbook spring-block result from the NCERT chapter on oscillations. As a plausibility check, a stiff spring with a modest mass should oscillate quickly, and a sub-second period is consistent with the relatively large stiffness of 200 N/m.