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soln1 - Physics 315 Oscillations and Waves Homework 1...

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Unformatted text preview: Physics 315: Oscillations and Waves Homework 1: Solutions 1. The body will fly off the diaphragm whenever the diaphragm’s downward acceleration exceeds the acceleration, g , due to gravity. Hence, as the fre- quency increases, the body will first fly off the diaphragm when the maxi- mum downward acceleration becomes equal to g : i.e. , ω 2 a = g, Here, ω = 2 π f is the diaphragm’s angular frequency of oscillation, f is the same frequency in hertz, and a is the amplitude of the oscillation. It follows that f = 1 2 π radicalbigg g a . However, a = 1 × 10- 5 m and g = 9 . 8 m s- 1 , so f = 157 . 6 Hz. 2. Let x 1 and x 2 be the extensions of the first and second springs, respectively. The forces exerted by these springs are f 1 = − k 1 x 1 and f 2 = − k 2 x 2 , re- spectively. If the springs are connected in parallel then x = x 1 = x 2 , where x is the downward displacement of the mass with respect to its equilibrium point. However, if the springs are connected in series then x = x 1 + x 2 . If the springs are connected in parallel then f = f 1 + f 2 , where f is the down- ward force acting on the mass due to the springs. However, if the springs are connected in series then f = f 1 = f 2 . (N.B. f 1 equals f 2 because of Newton’s third law of motion.) The generic equation of motion isNewton’s third law of motion....
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soln1 - Physics 315 Oscillations and Waves Homework 1...

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