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homework1

# homework1 - Homework Set 1 Due Thursday 06/30 Problem 1 A...

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Homework Set 1 Due Thursday, 06/30 Problem 1 : A spring has a relaxed length of 15.0cm. When a 100g mass is hung from the spring, the spring is stretched to 17.5cm. When an unknown mass M is hung from the spring, the spring stretches to 18.0cm. (a) What is the mass of M? (b) What is the frequency of oscillations with the 100g mass and with mass M? (c) If a 250g mass is attached to the spring while the spring is relaxed, and then dropped from that position, what will be the amplitude of the oscillations? Problem 2 : The position of an oscillator is given by (a) What is the amplitude, angular frequency, frequency and period of the oscillations? (b) What is the speed of the oscillator at t = 0 ? (c) If the oscillator has a mass of 0.05kg, what is the spring constant? Problem 3: A cylindrical barrel with length L = 0.40m, radius R = 0.15m and density ρ = 600 kg/m 3 floats in water (density 1000 kg/m 3 ). The forces acting on the barrel are gravity, pointing down, and the buoyant force, equal to the weight of the displaced water according to Archimedes' law, pointing up.

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