A)When the bucket is half full, find the period of oscillation. B)When the bucke

Question

A)When the bucket is half full, find the period of oscillation. B)When the bucket is half full, find the rate at which the period is changing with respect to time. C)Is the period getting longer or shorter? D)What is the shortest period this system can have? A)When the bucket is half full, find the period of oscillation. B)When the bucket is half full, find the rate at which the period is changing with respect to time. C)Is the period getting longer or shorter? D)What is the shortest period this system can have? B)When the bucket is half full, find the rate at which the period is changing with respect to time. C)Is the period getting longer or shorter? D)What is the shortest period this system can have? C)Is the period getting longer or shorter? D)What is the shortest period this system can have? D)What is the shortest period this system can have?

Explanation / Answer

T = 2(pi) Sqrt(m/K) and we known that dm/dt = -2x10^-3 kg/s, and the rate of change of the period is dT/dt A) when the bucket is half full, m = 5.5kg (half the water is empty) + 2.2 (weight of the bucket) = 7.7kg Therefore, T = 2(pi) x Sqrt(7.7/120)=1.59 B) DT/dt = pi/Sqrt(mK) dm/dt Therefore, DT/dt = pi / (Sqrt(7.7x120)) x -2x10^-3= 0.101 C) as DT/dt is negative, the period is getting shorter D) the bucket is empty, so m=2.2kg. Therefore, T = 2(pi) x Sqrt(2.4/120)= 0.888

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