1B If the stick is pivoted about point P a distance h = 10 cm from the center of mass, the period of oscillation is equal to (in seconds)

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1 05/07/03 HYSICS 3 Exa #1 Use g 10 /s in your calculations. NAME Feynan lease write your nae also on the back side of this exa 1. 1A A unifor thin stick of ass M 0. Kg and length 60 c is pivoted at one end. he period of oscillation for sall angular displaceents is equal to (in seconds) a) 0.4π b) π c) 4 d) 0.5 π e) NA 1B If the stick is pivoted about point a distance h 10 c fro the center of ass, the period of oscillation is equal to (in seconds) a) 0.4π b) π c) 4 d) 0.5 π e) NA CM 60 c CM QUESION 1A QUESION 1B. A A wave on a string is described by a function of the for y( x, A COS( kx ω. At one specific point of observation x x0 the tie between successive crests is 0. seconds. Which of the following is true? a) he wavelength is 5 b) he frequency is 5 Hz c) he speed of propagation is 5 /s d) he wavelength is 0. e) here is not enough inforation to justify any of the stateents above B A wave on a string is described by y(x, (0.001) COS ( x + 314s -1 t ) a) In what direction does it travel? Answer +X or -X Circle your answer b) he speed of the wave is equal to: Answer 5 _ ( in units of /s )

2 3. Consider a daped siple pendulu of length 0.4 with a quality factor Q A he angular frequency "ωο" of the oscillations (in units of rad/sec) is (round your answer to the closest integer nuber): a) 5 b) 100 c) d) π e) Unknown, because the value of the ass is not given g 3B How long does it take for the aplitude (assued sall) to decrease down to one-third of its initial value. Answers given in units of seconds a) 573 b) 195 c) 176 d) 40 e) NA 4. 4A hree physical pendulus A, B and C, of asses M A 0, M B 0 and M C 3 0 respectively, have the sae shape and the sae diensions. Rank the asses according to the periods of the pendulus, greatest period first Answer all tie 4B. hree physical pendulus consisting of identical unifor spheres of the sae ass that are rigidly connected by identical rods of length and negligible ass. Each pendulu is vertical and can pivot about suspension point. Rank the pendulus according to period of oscillation, greatest first. Answer a) c) b) a) b) c) Figure for question 4B only 5. A block whose ass is 680 g is fastened to a spring whose spring constant k is 65 N/. x0 defines the equilibriu position. he block is pulled a distance x 11 c fro its equilibriu position on a frictionless surface and released fro rest at t0. 5A Give an expression for the position of the block as a function of tie x( (0.11 ) COS (9.8s -1 (in eters) 5A Find the MECHANICA ENERGY of the oscillator E 0.39 (in Joules)

3 6. he figure below shows a 0.5 eter long string (with one end attached to the wall) of linear ass density 100 g/, under a tension of 1.6 N. At one end a person shakes the string up and down with an aplitude of 4 c. hysics 3 student 6A 6B he speed of the reflected waves traveling along the string is: a) 4 /s b) 0.1 /s c) 5 /s d) /s e) NA he person shakes the string with either 5 Hz or 6 hertz (one case at a tie). Indicate which expression is correct: a) Both cases satisfy the conditions to establish resonant standing waves in the string b) Since the reflected waves travel at a different speed than the incident wave, no resonance pattern is possible to establish along the string. c) Since only one end of the string is fixed, no resonant standing wave can be set in the string. d) Only one case satisfies the conditions for a resonant standing wave e) NA 7. A string of length 3 and linear ass density kg/ is fixed at both ends. One of its resonance frequencies is 5 Hz. he next higher resonance frequency is 336 Hz 7A Sketch in the space provided the first, second, third and fourth resonance wave patterns (see graphs in the corresponding lecture notes) 1st nd 3rd 4th 7B he fundaental frequency f 1 is equal to (in Hz) a) 5 b) 84 c) 336 d) 53 e) NA

4 1 8. For the "WAVE EQUAION" 0 v, where v 3 /s 8A By explicitly calculation of the derivatives of y, find out if the function y(x, (0.3) COS ( x + 314s -1 t ) satisfies the wave equation given above. (Write down the derivatives in the space provided below) y 1 v t y 8B Indicate if the function y(x, (0.0) COS ( 4-1 x - 1s -1 t ) satisfies the wave equation given above. ANSWER: YES. BONUS QUESION (3 extra points) A ring of radius R0.1 and ass M 0.5 Kg is suspended fro a peg, as illustrated in the figure below. he period of oscillations is equal to: ANSWER: 0.9 sec Support Ring R

5 FORMUAS HA MIGH HE ω π f Siple endulu: eriod π Use g 10 /s g in this exa hysical endulu: eriod I π Use g 10 /s in this exa gh d x b d x k Daped siple haronic oscillator + + x 0 αt x( Ae COS( ωt + φ) b where ( b ) α ω ω 0 k ω 0 natural frequency of the oscillator Quality factor: Q ω0 b Where ω 0 is the natural frequency of the oscillator ω ( 0 Q In ters of Q the solution is expressed as: x( A COS( t + ) e ω φ Waves traveling along a string: speed v µ

5/09/06 PHYSICS 213 Exam #1 NAME FEYNMAN Please write down your name also on the back side of the last page

5/09/06 PHYSICS 213 Exam #1 NAME FEYNMAN Please write down your name also on the back side of the last page 5/09/06 PHYSICS 13 Exa #1 NAME FEYNMAN Please write down your nae also on the back side of the last page 1 he figure shows a horizontal planks of length =50 c, and ass M= 1 Kg, pivoted at one end. he planks