More practice questions

4. Q4. The amplitude of an oscillator is halved. What happens to its total energy?

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   E = ½kA^² goes as A^², so it falls to a quarter.

5. Q5. At what displacement is the kinetic energy three times the potential energy?

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   ½k(A^² − x^²) = 3 × ½kx^² gives A^² = 4x^², so x = ±A/2.

6. Q6. A 1 kg block on a spring oscillates with amplitude 0.1 m and total energy 0.5 J. Find the spring constant and the period.

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   k = 2E/A^² = 2 × 0.5/0.01 = 100 N m^⁻¹. Then ω = √(100/1) = 10 rad/s and T = 2π/10, about 0.628 s.