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String fixed at both ends vibrates in three segments: amplitude of the particle velocity

The same question, asked 2 times: 19 Apr 2025 S1*, 13 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    19 Apr 2025 S1

    27
    A string of mass 0.1kgm−10.1kgm^{- 1} has length 0.9 m. It is fixed at both ends and stretched such that it has a tension of 40 N. The string vibrates in three segments with amplitude 0.3 cm. The amplitude (maximum) of the particle velocity is (in m/sm/s )

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  2. Question 2

    13 May 2026 S2

    121
    A spring of mass 0.20.2 kg/m has length l=0.6l = 0.6 m. It is fixed at both ends and stretched such that is has a tension 8080 N. The string vibrates in three segments with amplitude 0.50.5 cm. The amplitude of transverse (particle) velocity is

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