mat-sln-asn-hwk26-spr02

mat-sln-asn-hwk26-spr02 - Total Points for Problem: 1...

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Solution for Homework 26 Periodic Motion I Solution to Homework Problem 26.1() Problem: What does the position vs. time curve of a simple harmonic oscillator look like? Solution A sinusoidal function. The most general form is x ( t ) = A sin ωt + B cos ωt Where the constants A and B are determined by initial conditions ( x 0 and v 0 ). This function can also be expressed as ( C and φ are constants determined by initial condition) x ( t ) = C cos( ωt + φ ) or x ( t ) = C sin( ωt + φ ) Total Points for Problem: 1 Points Solution to Homework Problem 26.2() Problem: What will be the eFect of increasing the strength of the restoring force in an oscillating system? Solution The period of the given oscillation will decrease when the restoring force is increased (and if the restoring force is decreased, the period will increase). A stronger spring means the mass will oscillate faster.
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Unformatted text preview: Total Points for Problem: 1 Points Solution to Homework Problem 26.3() Problem: Explain what each term in the following equation for the position of a simple harmonic oscillator represents: x ( t ) = A sin( t + ) Solution A is the amplitude (maximum displacement), is the angular frequency of oscillation, t is the time at which the position is being evaluated, and is the initial phase at time t = 0 . Total Points for Problem: 3 Points Solution to Homework Problem 26.4() Problem: What quantities does the angular frequency ( ) of a simple pedulum depend upon? Solution The length of the string, and the gravitational acceleration. = r g Total Points for Problem: 4 Points...
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