Lab 10 - Oscillations

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Jan 9, 2024

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Save your work frequently! Name_______________________________________________ Section______________________ LAB: OSCILLATIONS Learning goals: Determine amplitude, period, and frequency. Translate among representations (pictures, graph, and equation) for simple harmonic motion Reason qualitatively and quantitatively with the expression for period of a mass on a spring. Apply energy ideas to simple harmonic motion. Simulation: oPhysics - Simple Harmonic Motion: Mass on a Spring http://ophysics.com/w1.html Investigation 1: Force and Motion Perspective Consider a block attached to spring moving on a frictionless horizontal surface as shown. Uncheck the following boxes on the simulation. Show Energy Pie Graph Show Energy Graph Show Time Graphs Show Numerical Values x = 0 is the equilibrium position where the spring is at its resting length. The block is released at its max stretch where x initial = 5.0 m, it then oscillates between x max = 5.0 m and x min = -5.0 m. The mass of the block is 10 kg and the spring constant of the spring is 80 N/m. Click “Run”. You can slow down or speed up the simulation by choosing the Animation Speed. A. Pause the simulation when the block first passes (approximately) x = +1.0 m (while moving to the left), 1. is the block speeding up, slowing down , or moving with constant speed ? The block is slowing down with constant speed. This is because the spring consant is slowing it down to not move as fast. 2. Draw arrows in the boxes below to show the direction of the velocity of the block, the acceleration of the block, and the force of the spring on the block. 1
Save your work frequently! B. When the block first reaches x = -5.0 m (that’s as far to the left as it goes), Draw arrows in the boxes below to show the direction of the velocity of the block, the acceleration of the block, and the force of the spring on the block. Show the relative magnitudes compared to x = +1.0 m by drawing longer or shorter arrows. C. When the block next passes (approximately) x = +1.0 m (while moving to the right), a. is the block speeding up, slowing down , or moving with constant speed ? Slowing Down with constant speed b. Draw arrows in the boxes below to show the direction of the velocity of the block, the acceleration of the block, and the force of the spring on the block. D. Determine an equation that describes the position of the block as a function of time. T = 2pi/(k/m)^1/2 E. Draw the x-t, v-t, and a-t graphs. F. Check with the simulation by checking the “Show Time Graphs” box. Reconcile any discrepancies 2
Save your work frequently! between your answers and your observations. Investigation 2: Energy Perspective A. When the block first passes (approximately) x = +1.0 m (while moving to the left), 1. Is spring potential energy positive, negative, or zero ? Is it increasing or decreasing ? Spring potential energy is always psotive and it is increasing since there is kinetic energy being coverted into ptotential energy because of the spring. 2. Is kinetic energy positive, negative, or zero ? Is it increasing or decreasing ? The kinetic energy is also positive and is decreasing since it is being converted to potential energy by the spring. B. When the block next passes (approximately) x = +1.0 m (while moving to the right), 1. Is spring potential energy positive, negative, or zero ? Is it increasing or decreasing, or staying the same ? The potential energy is increasing and positive. The kinetic energy is being converted to potential energy where it will then go in the opposite direction. 2. Is kinetic energy positive, negative, or zero ? Is it increasing, decreasing, or staying the same ? The kinetic energy is positive and decreasing and being coverted to potential energy. C. At what location(s) is (are) 1. spring potential energy zero ? X=0 2. spring potential energy greatest? -xmax and xmax 3. kinetic energy zero ? -xmax and xmax 3
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Save your work frequently! 4. kinetic energy greatest? X=0 D. Using your answers to the above, sketch a qualitatively correct graph of spring potential energy vs. position. Label it U sp . (It may help to recall the expression for spring potential energy – What shape graph would you expect?) E. On the same axes, sketch a qualitative graph of total mechanical energy vs. position. Label it ME. (It may help to consider: Is there any work done on the system consisting of the block and the spring during the motion?) F. On the same axes, sketch a qualitative graph of kinetic energy vs. position. Label it K . (It may help to consider: are kinetic and spring potential the only forms of energy that change in these processes?) G. Check with the simulation by checking the “Show Energy Graph” box. Reconcile any discrepancies between your answers and your observations. 4
Save your work frequently! Investigation 3: Quantitative Reasoning Pay attention to the signs, recall that to the right is positive and to the left is negative. A. When the block is at x = +5.0 m (x max ), fill out the following table. Show your work! Position (m) 5 Velocity (m/s) 0 Acceleration (m/s 2 ) -40 Spring force (N) -400 Kinetic energy (J) 0 Potential energy (J) 1000 Mechanical energy (J) 1000 B. When the block is at x = 0 m (while moving to the left), fill out the following table. Show your work! Position (m) 0 Velocity (m/s) -14.15 Acceleration (m/s 2 ) -.606 Spring force (N) -6.06 Kinetic energy (J) 1000 Potential energy (J) 0 Mechanical energy (J) 1000 5
Save your work frequently! C. When the block is at x = 0 m (while moving to the right), fill out the following table. Show your work! Position (m) 0 Velocity (m/s) 14.15 Acceleration (m/s 2 ) -2.7 Spring force (N) -27 Kinetic energy (J) 1000 Potential energy (J) 0 Mechanical energy (J) 1000 D. When the block is at x = -5.0 m (x min ), fill out the following table. Show your work! Position (m) -5 Velocity (m/s) -4.5 Acceleration (m/s 2 ) 40 Spring force (N) 400 Kinetic energy (J) 0 Potential energy (J) 1000 Mechanical energy (J) 1000 E. When the block is at x = +1.0 m (while moving to the left), fill out the following table. Show your work! Position (m) 1 Velocity (m/s) -13.8 Acceleration (m/s 2 ) -8.46 Spring force (N) -86 Kinetic energy (J) 950 Potential energy (J) 50 Mechanical energy (J) 1000 F. When the block is at x = -1.0 m (while moving to the right), fill out the following table. Show your work! Position (m) -1 Velocity (m/s) -13.8 Acceleration (m/s 2 ) 10 Spring force (N) 100 Kinetic energy (J) 950 Potential energy (J) 50 Mechanical energy (J) 1000 6
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Save your work frequently! G. Check with the simulation by checking the “Show Numerical Values” box. Reconcile any discrepancies between your answers and your observations. Investigation 4: Oscillation A. What is the period of the oscillations? What is the frequency? Show your work and check the simulation. T = 2pi*sqr(m/k) T= 2pi*(1/2root2) T=pi/(2)^1/2 T= x = pi 2 F= 1/t = 2 /pi B. What is the period if you decrease the “initial Spring Stretch” to 2.5 m? Show your work and check the simulation. T = 2pi*sqr(m/k) T= 2pi*(1/2root2) T=pi/(2)^1/2 T= x = pi 2 Initial strectch does not effect T. C. What is the period if you decrease the “Mass of Block” to 5.0 kg? The “initial Spring Stretch” is set back to 5.0 m. Show your work and check the simulation. T = 2pi*sqr(5/80) T= 2pi*(1/4) T=pi/2 T= x = pi / 2 D. What is the period if you decrease the “Spring Constant” to 40 N/m? The “initial Spring Stretch” is set back to 5.0 m and the “Mass of Block” is set back to 10 kg. Show your work and check the simulation. E. T = 2pi*sqr(10/40) F. T= 2pi*(1/2) G. T=pi/(2)^1/2 7
Save your work frequently! H. T= x = pi / 2 8