# hwk26 - Solution for Long-answer Homework 26 Periodic...

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Unformatted text preview: Solution for Long-answer Homework 26 Periodic Motion problems Solution to Long-answer Homework Problem 26.1() Problem: A 1 kg mass is on a light spring. You pull the mass so it undergoes simple harmonic motion with an amplitude of 12 cm . It has a maximum acceleration of 5 . m s 2 . What is its total energy? Solution The energy in a mechanically oscillating system is given by Eq. 16 . 14 , E = 1 2 mω 2 A 2 So we need to find ω . We are given the maximum acceleration, which is also a max = Aω 2 So ω = radicalbigg a max A And so we have E = 1 2 mA 2 parenleftBig a max A parenrightBig = 1 2 mAa max E = 1 2 (1kg)(0 . 12m) parenleftBig 5 . m s 2 parenrightBig = 0 . 30J Total Points for Problem: 4 Points Solution to Long-answer Homework Problem 26.2(Masses on spring ) Problem: Consider a spring hung vertically from the ceiling. (a)A mass is attached to a k = 196 N m spring. It then undergoes simple harmonic motion with a period of 2 5 seconds. What is the inertia of the mass? (b)You pull the mass in part so it undergoes simple harmonic motion with an amplitude of 10 cm . What is its maximum acceleration and velocity? (c)Taking upward to be positive, at what position in the motion do the maximum position, velocity and acceleration occur? (d)If we call the time where it is first passing through the equilibrium position on the way up t = 0 , write an equation of motion for the oscillation, x ( t ) = ?, identifying the values of all constants that?...
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hwk26 - Solution for Long-answer Homework 26 Periodic...

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