More practice questions

4. Q4. What spring constant makes a 0.1 kg block oscillate at 2 Hz?

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   ω = 2πν = 4π rad/s, so k = mω^² = 0.1 × (4π)^², about 15.8 N m^⁻¹.

5. Q5. A 0.5 kg particle performs SHM of amplitude 0.1 m and period 1 s. Find the largest restoring force on it.

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   The force is largest at the extremes: F = kA = mω^²A = 0.5 × (2π)^² × 0.1, about 1.97 N.

6. Q6. A particle’s acceleration is a = −π^²x (SI units). Find its period.

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   ω^² = π^², so ω = π rad/s and T = 2π/π = 2 s.