Please show work to determine: a) the force constant of the spring b) the maximu

Question

Please show work to determine:

a) the force constant of the spring

b) the maximum speed of the block

Question 1: One-Spring System Open and run the simulation to see a 1.0kg block vibrating on a horizontal frictionless surface. Based on your observations and reasoning, determine the force constant of the spring and the maximum speed of the block. If you need help (give it a good try on your own first), consult the Advisor. 9.8 One-and Two-Spring Vibrating Systems: Question 1 Force Constant of Spring You can determine the frequency from the time measurement. You know that the block has a mass of 1.0kg. Now, can you find the force constant of the spring? Maximum Speed of the Block Once you have found the force constant of the spring, you can measure the amplitude of the vibration by watching the simulation. Then you can calculate the energy of the vibrating system. You also know that the block has a mass of 1.0kg. Now can you find the maximum speed of the block?

Explanation / Answer

according to the image given at 10 sec block came to its original position that means it has completes one oscillation

so its time period = 10 sec

time period = 2 * pi / sqrt(k / m)

10 = 2 * pi / sqrt(k/1)

k = 0.39478 N/m

force constant of the spring = 0.39478 N/m

energy stored in the box = 0.5 * k * amplitude

amplitude = 3.5 m (from image)

enery = 0.5 * 0.39478 * 3.5^2

energy = 2.418 J

energy = 0.5 * m * v^2

2.418 = 0.5 * 1 * v^2

v = 2.19909 m/s

maximum speed of the block = 2.19909 m/s

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