A steel strip, clamped at one end, vibrates with a frequency of 20 Hz and an amplitude of 5 mm at the free end, where a small mass of 2 g is…

Source: JAMB · 2024

A steel strip, clamped at one end, vibrates with a frequency of 20 Hz and an amplitude of 5 mm at the free end, where a small mass of 2 g is positioned. Find the maximum kinetic energy of the mass.

  1. 1.84 × 10⁻⁴ J
  2. 4.28 × 10⁻⁴ J
  3. 2.17 × 10⁻⁴ J
  4. 3.95 × 10⁻⁴ J ✓
Explanation

The mass at the free end moves in simple harmonic motion. Its speed is greatest at the centre, where KE is maximum.

Maximum speed v = ωA = 2πfA = 2π × 20 × 0.005 ≈ 0.628 ms⁻¹.

Maximum KE = ½mv² = ½ × 0.002 × (0.628)² = 0.001 × 0.3948 ≈ 3.95 × 10⁻⁴ J.

Remember to convert 2 g to 0.002 kg and 5 mm to 0.005 m.

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