Question

Please show step by step explanation including all units.

Part 1 Mass and Spring System

You have a spring with an unknown spring constant. You attach a
10 gram mass and note that the spring stretches 1 cm. Then you
remove that mass and attach a 20 gram mass and note that the spring
stretches 2 cm. a) Find the slope of the line on F vs. x plot. That
will be your spring constant. b) Then you pull the mass (10 gram
mass) down and release it, the mass oscillates up and down. You
observer that it takes 2.0 seconds for the spring to go up and down
10 times. Then you do the same for the 20 gram mass, and it takes
2.83 seconds for 10 oscillations. Plot T^{2} vs. mass. The
slope of this line is the spring constant. How does this spring
constant compare with the one you found in part a)?

Part 2

You have a pendulum in which the length of the two strings is 10 cm and 20 cm.

It takes 6.3 seconds for the pendulum to go back and forth for the 10 cm length,

and 9.0 seconds for ten oscillations for the 20 cm length. Plot
the square of the period vs. the length of the string. Compute g
using the slope of this line. How does it compare with 9.8
m/s^{2}?

Answer #1

slope = 9.8

Therefore, spring constant = 9.8 N/m

b)

for 10 g mass

T = 2/10 = 0.2 seconds

T^2 = 0.04

for 20 g mass

T = 2.83/10 = 0.283 seconds

T^2 = 0.080089

Slope = 4.0089

Therefore, spring constant = 4 * pi*pi/slope

= 4 * 3.14 * 3.14 /4.0089

= 9.87

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