Question

Question 3: "Simple” Harmonic Motion As a skeptical physicist, you decide to go to the lab to test whether or not masses on springs really exhibit simple harmonic motion. You attach a large block of mass m = 0.5 kg to the biggest spring you can find. You setup this over-sized experiment so that the mass is oscillating horizontally, an ultrasonic sensor is used to measure its motion - the resulting data is plotted in figure 3. Assume that there is no damping. Figure 2: The displacement vs. time graph generated by your data logger. a) Using figure 3, find the period of oscillations, the amplitude, and the equilibrium position. b) Sketch the acceleration vs. time graph for this system (from t = 0s to t = 5s). c) Choose any time that you like and calculate the total energy of the system at that moment. Ignore gravity. d) As the mass continues to oscillate, how do you expect this value for the total energy to change? e) If now there is some damping in the system, with a damping coefficient b = 0.2 kg/s, how long will it be until the mass loses 30% of its amplitude?

Answer 1

ferest of all 9 tried to write the con cf motion a(4), 9 choose another co-ordinate Ryslem (x', f') fore simplicity, such that 14', ') = (2.5m, 25.8) In {x',t!) the X (f) shows cosine nature X2102 2017) using translation of co-ordinate system, (-2,5) = 2008 $2764-205)? I cas period of oscillation is the time taken to repeat the motion or simply I choose time gap between two consecutive groups. troughs A&B. T. 45 - 13 3.sec. med point Equilibrium posétècn is the distance between extreme positions (crest & trough ) ;. &qm position és 2.5 m.

position all * 2.2.5 Amplitude is distance between og extreme positden. A: 2m . 6) WHEDE, 2 20 x I-sin 7 04. die 2V??y ?xvf-cox21? y 21 y ? (-2,5) ģ ro3 - > (2 ) 5 sec - t. (dec) . ( Tola con trở 1 : 1 Menu - XE | PE -Ź med? + Kx? extension en spring. - where xo is

(c) from graph - vel. at eam eam time = 1,75861. - 2x 27 x Rin ( 27 ( 1.75 -2.5) 2 0.3444 m/s ; E. KEEPEE ļ (05) (0.3445) to 0.0296700 Toul dl gf is conserved (töme independent). (el 3n demping oscillatzen, X= A expl be 102 wf 2m » 2 = eup (-bt) cosef fore x = 70% of A; => fa 2.496.80C. i Amplitude well derease by 30% after 2.49 6 sec