Calculating Power for a Vibrating String

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To calculate the power required for a vibrating string with a linear mass density of 0.143 kg/m and tension of 107 N, the wave speed (V) and angular frequency (ω) were determined using relevant equations. The amplitude is given as 1.97 cm and the frequency is 107 Hz. There is a suggestion that the question might be better framed in terms of energy rather than power, as the problem does not indicate any energy dissipation. The discussion emphasizes the assumption of no energy loss, allowing for continuous vibration. The next step involves calculating the string's kinetic energy at minimum amplitude to further analyze the power requirement.
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Homework Statement



A string with linear mass density of 0.143 kg/m is under a tension of 107 N. How much power must be supplied to the string to generate a sinusoidal wave of amplitude 1.97 cm and frequency 107 Hz?




Homework Equations



V=√F/μ
V=ω.A


3. The Attempt at a Solution

I found V and ω by using equations above but don't know how to calculate power.


 
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The question should probably be rephrased "How much energy..." rather than "How much power..." With nothing in the problem's statement describing how the string might dissipate energy, I'd assume there's no energy loss at all -- the string vibrates forever. Try calculating the string's kinetic energy as it passes through minimum amplitude.
 
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