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Problem 1: Oscillation Problem Part 1: A spring that you find in the lab is characterized by the graph below. A. What is the unstretched length for the spring? B. What is the spring constant for this springi C. Write the equation that describes the spring force Fup in terms of the spring length L sp Part 2: The spring is then attached to an object with a mass of 101 grams (friction can be ignored). The object is pulled to the right, placing the object 20.0 cm away from equilibrium. r trac D. What is the value of force that the spring exerts on the cart when pulled to this distance? E. How much elastic potential energy is stored in spring when pulled to this distance?
Part IlI The cart is then let go and allowed to oscillate. What is amplitude, period and frequency for this oscillation? eraw an energy vs. position graph and clearly label energy and position values on the graph and clearly identify the equilibrium and turning points. What maximum speed will this amount of energy correspond to? Where will this maximum speed occur? H. Finally, draw accurate position vs. time and velocity vs time graphs. Clearly label the period and maximum values on each of these graphs. Write equations that describes these graphs. I. io
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Spring is unstretched when the extemal force acting on the spring is zero From the observation from the graph, the upstretched length of the spring is 0.3 m The spring constant is the slope of the straight line on the graph. 5-0 0.62-0.3 0.32 -15.625 N/m Thus, the spring constant for the spring is 15.625 N/m Write the equation of spring force. (F-0)-k(x-0.3) Substitute the given values in the above expression F 15.625x-15.625 x 0.3 F 15.625x-4.6875Thus, the equation of the spring force is F 15.625x-4.6875 D) Calculate the stretched length. x 0.3 +0.2 -0.5 m Write the expression for the spring force. F 15.625x0.5-4.6875 -3.125 N Thus, the spring force is 3.125 N Write the expression for the elastic potential energy stored in the spring E=-102 Substitute the given values in the above expression E-x15.625x0.52 1.953 J Thus, the energy stored is 1.953JWrite the expression for the equation of motion Suppose the harmonic motion is defined by, x- Asin (ot) -Ao sin (øt) Substitute the given values in equation (1) 15.625Asin()0.101-Asin (o0 15.625 0.101 12.44 rad/s ω Thus, the frequency is 12.44 rads Write the expression for the time period 2π Substitute the given values in the above expression. 12.44 rad/s -0.5051 sThus, the period is 0.5051s Write the SHM equation. 0.5 Asin (12.44x0.5051) 0.5 0.1094 -4.57 m Thus, the amplitude is 4.57 m The Figure-(1) shows the graph.Figure-(1) Write the expression for the energy balance Substitute the given values in the above expression 15-625x(0.5). 0.101 嗌訌 38.68 6.22 m/s Thus, the maximum speed is 6.22 m/s The maximum velocity occurs at equilibrium position The Figure-(2) and Figure-(3) shows the graphsFigure-(2)Figure-(3)

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