Lab#21: Mass-Spring Oscillations

Mass-Spring Oscillation

Samuel
Ellis
Mia
11-23-2016

Purpose:

To determine the oscillation of the spring with different weight and compare it to see if simple harmonic equation is accurate.

Theory:

Based on simple harmonic equation, we know that spring and pendulum have same oscillation. And we know that oscillation is based on how much the spring stretched. When releasing spring and weight dropped, the up and down motion is determined by the spring constant. Since we have different spring with different spring constant, we can use oscillation equation to predict it period. 

Procedure:

1. Mount clap on the table, with a rod horizontal respect to the table. 

2. Hang a spring on the rod.

3. Hang 5 different weigh on it and record it period and mass.

4. Find spring constant of the spring.

Measured Data:

Data for Spring 4

m = 215 g

t_1 = 6.66 sec, t_2 = 6.63 sec, t_3 = 6.62   t_average = 6.64 sec

m = 315 g

t_1 = 8.05 sec, t_2 = 8.00 sec, t_3 = 8.08 sec  t_average = 8.05

m = 4.15 g

t_1 = 9.23 sec, t_2 = 9.21 sec, t_3 = 9.21 sec  t_average = 9.21 sec

m = 65 g

t_1 = 3.63 sec, t_2 = 3.62 sec, t_3 = 3.65 sec  t_average = 3.63 sec

Spring for All Group

Calculation:

Predicted value:

T = 2*pi*sqrt(m/k)

T = 2*3.14*sqrt(0.115/19.4)

T = 0.48 sec

Measured value:

T = time/how many times

T = 5.22/10

T = 0.522 sec

Analysis:

1. We calculate our spring by using spring potential energy equation, 0.5*k*x^2. k is spring constant and x is how much it stretch. 

2. 

3.  

5. Our spring constant is right. But if k is off by 5% or more, my first option will go with period. Usually we measure period for at least 3 times and those time should somewhere similar to each other. We then average those number to get most accurate data. However, when averaging 3 different number, there's will be uncertainty, and that's where those error come from.

6. According to our formula, period(T) = 2*pi*sqrt(m/k). In this case, m is mass & k is spring constant. k = (2*pi*m)/T. since 2*pi is constant, we can simply ignore it when determining variables. Since k = m/T(when ignoring 2*pi), when T is decreasing, it will make m divide by smaller number, which will have bigger product. In this case, it will be k. 

7. Use the same equation from above, k = m/T. We know that if we increase the mass(m), then k will become bigger number. Since m is increasing, bigger number divide by smaller number result in bigger resultant value. Therefore, when increasing period, mass is also increase.

Conclusion:

In this experiment, we used simple harmonic equation to find the period and spring constant of the spring. We used different weight and make it oscillating so we make sure our spring constant is the same. Thus, we used the same equation to calculate it period. However, the number we got are little bit different from the actual measured data. 0.48(calculated value) verses 0.522(measured value). And that difference might due to the rounding error of the measured period or the human error when stopping the timer.