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13 FRQ-the horizontal spring (20 points) Two identical masses of mass M are attached to an ideal spring positioned horizontally on a frictionless surface, as shown below. Jum 7, The system stretched to the right a distance xo and released to oscillate in simple harmonic motion. A motion sensor is used to capture the velocity-time graph of the oscillating masses. The graph of this motion is shown below. vel m/s 10.5-4.5 6 sinx -1+05 1 15 2 25 3.5 4 4.5 5 5.5 6 6.5 8 8.5 9 9.5 10 10.5 time is a) Determine the time period, 7, the angular frequeny, a, the amplitude of the displacement, x, and the maximum acceleration, a,, of the oscillating system. T= w 6 21T X = A cos (wt) A wt = 2TT W: ZIT 21 TT A = 1 Aw².. ao - 3 (ड) b) i) Write the expression, using values from a) above, that describes the position of the system as a function of time. v(t) = -sinx P(t)=-COS X ii) Draw the position-time graph on the axes below. Annotate the axes with appropriate values. pos m Aftenfis 15 time /s -4 E CS Scanned with CamScanner 2 T= 6 seconds डु W = I 9₁ = () ²²
ID: E c) i) Write the expression, using values from a) above, that describes the acceleration of the system as a. function of time. v(t) = - Sinx all): cos x ii) Draw the acceleration-time graph on the axes below. Annotate the axes with appropriate values. ac m/s/s 4 10 time/s The force constant for the spring is known: k = 24.0 N/m. d) i) Calculate the maximum kinetic energy of the oscillating masses. ka² r ½ (24)(1)² = 12k15 ii) Plot a graph of kinetic energy as a fuction of time. Annotate the axes with appropriate values. KUJ time /s Later, when the system is again at maximum position, one of the masses is detached, as shown in the diagram below. 70 e) i) Describe the effect that this loss of mass has on the total mechanical energy of the system. Explain your reasoning. There is no relation between mass and mechanical energy ii) What effect does this loss of mass have on the time period of the oscillation? Explain your reasoning. the period will decrease 3 CS Scanned with CamScanner Name: ܩܣܝܝܝܝܝܝܐ kuw